I'll leave it to others with greater familiarity with the topic to address the first half your excellent question - that of western support for the Indonesian invasion of East Timor during the 1975 invasion of East Timor. I'll address the second half of your question, or at least part of it, by discussing Australian government investigation and response into the deaths of five of the six journalists you mention.
I also want to note that although I can discuss the circumstances surrounding the journalists' deaths and the subsequent developments into the investigaiton, I end this discussion with somewhat of a sucker-punch in that it falls afoul of the /r/AskHistorians No Current Events rule for me to delve into the modern politics of Australia-Indonesia relations and their influence on the Australian government stance on the deaths of the Balibo Five.
Context
Five Australian journalists (hereby the 'Balibo Five') were killed in the East Timorese town of Balibo on October 16, 1975, two months before the commencement of Operation Lotus and the 'official' beginning of the Indonesia invasion of East Timor on December 7, 1975. Their bodies were then incinerated and their remains disposed of by Indonesian forces.^1 The circumstances surrounding the deaths of these journalists is heavily contested - the official Indonesian stance is that they were killed in crossfire as Indonesian special forces fought with East Timorese forces during a border incursion. This stance is not contested by the Australian government, however successive investigations by the UN Transitional Administration in East Timor (UNTAET, "The UNTAET Investigation") in 2001 and a comprehensive 2007 Coronial Inquest into the death of Brian Raymond Peters (one of the five journalists killed) headed by New South Wales Coroner Magistrate Dorelle Pinch ("The Peters Inquest") have established the overwhelming likelihood that the Balibo Five were not killed in crossfire during the Indonesian incursion into Balibo, but rather deliberately executed by Indonesian special forces to prevent the journalists reporting on the Indonesian attack. The clear dissonance between the Australian government's stance on the journalists' deaths and the findings of these investigations has been a major source of contention both in the Australian media and in Australia-Indonesia relations.^2
Findings of Inquests into the deaths of the Balibo Five
Here I'll seek to answer your question "why has the Australian government never fully inquired into the deaths of six reporters that were killed as a result of the invasion," with two caveats: Firstly, I'll only be addressing the deaths of the 'Balibo Five,' as that is the extent of my expertise. Secondly, I will be reinterpreting your question to discuss not only Australian government inquiries, but to discuss the official Australian government response to inquiries and stance to them.
There have, contrary to your suggestion, been seven inquests into the circumstances surrounding the killing of the Balibo Five by various bodies, including the Australian and Indonesian governments, the UN, and other independent third parties - the most significant of which I have highlighted above being the 2001 UNTAET Investigation and the 2007 Peters Report. In 2001, an ongoing UNTAET investigation into the deaths of the journalists and the actions of the Indonesia government in the lead up to Operation Lotus and the invasion of East Timor sought warrants for the arrest of Mohammad Yunus Yosfiah, Christoforus da Silva, and Domingos Bere, three Indonesian Ex-Army officials who had been linked to the journalists' killing.^3 The investigation additionally sought interviews with another nine individuals in relation to the killings, but was denied both the warrants and the interviews by the Indonesian government.^4 The Australian government was silent on the issue.
Public pressure for more comprehensive findings into the deaths of the Balibo Five remained following the stonewalling of the UNTAET investigation, and were a frequent theme in Australian media throughout the early 2000s. Ultimately, this pressure translated to a Coronial Inquest which would ultimately be released as the Peters Report in November, 2007. The comprehensive report concluded that:
"Brian Raymond Peters, in the company of fellow journalists Gary James Cunningham, Malcolm Harvie Rennie, Gregory John Shackleton and Anthony John Stewart, collectively known as “the Balibo Five”, died at Balibo in Timor- Leste on 16 October 1975 from wounds sustained when he was shot and/or stabbed deliberately, and not in the heat of battle, by members of the Indonesian Special Forces, including Christoforus da Silva and Captain Yunus Yosfiah on the orders of Captain Yosfiah, to prevent him from revealing that Indonesian Special Forces had participated in the attack on Balibo. There is strong circumstantial evidence that those orders emanated from the Head of the Indonesian Special Forces, Major-General Benny Murdani to Colonel Dading Kalbuadi, Special Forces Group Commander in Timor, and then to Captain Yosfiah."^5
Further, it recommended that:
"In light of the dissatisfaction about the status quo expressed by some of the families in the course of the inquest, I recommend that, as a matter of priority, the Australian Government liaise with the next-of-kin of the Balibo Five to ascertain, and facilitate, their wishes in respect of the continued internment of the remains of the journalists in Jakarta, Indonesia.
"A national industry-wide Safety Code of Practice for journalists should be developed in conjunction with, and endorsed by, Australia’s media organisations."
The Peters report was, in effect, a total rejection of the official Indonesian and Australian stance that the Balibo Five had been killed in crossfire during fighting over the town, and instead presented the case that the journalists had been deliberately executed in a war-crime against civilians, and that Indonesian forces had then deliberately acted to disguise evidence of their atrocity by incinerating the journalists' remains and instigating a cover-up, in collusion with the Australian government at the time.
The political and diplomatic implications of the Peters Report were explosive, with enormous furor in Australian media, a subsequent statement by opposition leader and later Prime Minister Kevin Rudd that "those responsible should be held to account" and that "You can't just sweep this to one side."^6 In 2009, the Australian Federal Police launched an official investigation into the deaths of the journalists, attempting to build on the findings of the Peters Report.
The Australian Government Response
Following the findings of the Peters Report and the subsequent public opinion storm over its implications, nothing happened. Rudd's implied promise to act on the Report's findings and hold those it identified as culprits to account failed to eventuate following his ascension to the Prime Minister's office, and he later drew criticism for his silence on the issue during a 2008 visit to Indonesia.^7 The aforementioned 2009 AFP investigation was dropped in 2014 with no action taken, following a failure to establish clear jurisdiction and a determination that there was "insufficient evidence to prove an offence."^8 The Australian government's position that the Balibo Five were accidentally killed in crossfire during fighting in Balibo on 16 October, 1975, remains unchanged.
Conclusion
I'm afraid to say that while discussion of the events of October 1975 and subsequent developments in the investigation into the deaths of the Balibo Five falls within the purview of this Subreddit, it would be in breach of /r/AskHistorians No Current Events rule for me to delve into the modern political dynamics between the two countries, and as such I'm unable to provide you with a particularly fulfilling conclusion. I do hope my discussion of the circumstances of their deaths, the subsequent investigations into those deaths, and the Australian government's response or lack-thereof to those investigations will nonetheless prove useful to you. The diplomatic relations of Australia and Indonesia form a key part of Australian international relations studies, and a wealth of information exists to discuss government responses to the Balibo Five from a modern international relations lens.
Thanks for reading, and I hope this helps.
With regards to the first part of your question, The Suharto regime in Indonesia had been an asset to Australia since shortly after the 1965-66 coup that instated him. Negotiations between President Suharto and Australia's Labor Party led to the 1972 Timor and Arafura Sea Treaty, which established the boundary between Australian and Indonesian territory in the seaways just north of the continent. These excluded a small region thenceforth known as "Timor Gap", as it belonged to East Timor, a Portuguese colony. West Timor had long been Indonesian, but maritime boundaries in the Timor Sea had been highly contended between Australia and Portugal since 1953. This set the stage for the 1975 invasion and 1976 annexation of East Timor. Despite leading to the deaths of 200,000 people, this oil rich parcel was a lucrative acquisition. Negotiations began immediately and although controversial culminated in the 1989 Timor Gap Treaty, which allowed Australian companies petroleum and mineral rights at a mere 10% tax to Indonesia. With this eventual outcome likely in the minds of the Labor Party in 1975, some may say they were imperialistically motivated.