The Carolingians had a master plan to reclaim the Kingdom of the Franks; their "Grand Strategy" began in the early 600s and culminated with the crowning of Charlemagne as the Holy Roman Emperor. How sound is this theory? Secondly, did any other families have similar "long-game" aspirations?

Well, although this comment is growing old, I'll pitch in my thoughts now that I've finally found time. As others have noted, OP is almost certainly representing the arguments of Bernard Bachrach, and the opening statement is an adequate summary of the introduction to Bachrach's Early Carolingian Warfare (2001). Bachrach is a respected senior scholar of early Carolingian studies, but I don't get the impression that he represents the consensus in the field in this regard (per /u/EMPEROR_JUSTINIAN_I's question). It might be useful to look at Bachrach's own opening example to see why other scholars are skeptical of some of his work.

Bachrach begins Early Carolingian Warfare by citing the Annals of Metz. This was a chronicle compiled sometime around 805, and it's the closest thing we have to a contemporary record of events. But as the Metz annalist compiled his history, he knew that Charlemagne would be crowned Holy Roman Emperor in 800, so he focused in on the events that led to that final outcome. Of course, this was 20-20 hindsight, and the Metz annalist omits a lot of the dead-end decisions that would have cluttered his work. Bachrach uses these observations to argue:

By the early ninth century, the notion of conceptualizing a long-term strategy was alien neither to the Metz annalist nor to the Carolingian court [the readers who were expected to understand this work]. Indeed, by imposing a long-term plan for the future on the past, the Metz annalist relied on the receptivity of his audience in the present (ca. 805) to the notion that detailed planning for the future in the long term was an established norm. (p. 4)

So basically, Bachrach noted that as the Metz annalist decided what to include and what to omit from his chronicle, he seems to have conceived of it all fitting into some sort of master plan. Most scholars would agree that early medieval historians and even chroniclers like the Metz annalist did indeed see of history conforming to a plan. But Bachrach suggests that this was a long-term political strategy—a human plan. In contrast, most other scholars now understand that, since almost every medieval author was trained in the church, the actual master plan was God's plan for salvation—something outside of human influence.

A historian was confronted by all the rough and tumble business of human affairs, and he or she needed to make sense of how all this conformed to God's plan as laid out in the Bible. For Bede, as he wrote his Ecclesiastical History of the English People—which established many of the norms for later Carolingian historians—this meant that he wanted to show how the English Church was moving along the path prescribed by the Acts of the Apostles. For many writers within the Carolingian Age itself, as they wondered how to make sense of the alliance between their king and the pope, the natural reference point was the kingdoms of the Old Testament. Charlemagne's coronation as Holy Roman Empire was an unholy meddling of the church in temporal affairs (an opinion that would become more popular during the later Investiture Controversy). It was instead a modern-day renovation of David's divinely-ordained kingship.

So if that's how we understand writers like the Metz annalist, what does that tell us about families like the Carolingians? It is of course possible that they began working in the early 600s to transform the people of the Franks into a new Israel with their own family at its head ... but I don't think so. I haven't seen any evidence to support this. Nobody talked about a Frankish king becoming the new David until Charlemagne had already made it an accomplished fact and churchmen sought to explain and justify their emperor's new position. And to presuppose that a minor lord in the 600s suddenly developed this ambition and then passed it on from generation to generation until it was achieved 200 years later? That seems all too incredible for me.

I think the best upshot of Bachrach's work is that it forces us to consider how early medieval authors were in fact thinking in terms of the long-term unfolding of history. It raises questions about how these long-term perspectives changed—and we know that they did. Quality studies of the many chronicles from the Carolingian period show that many of these authors, as they thought about the long-term sweep of history, were actually trying to figure out the direction of their own present-day events. And as situations changed, so too did the rulers' long-term goals, with at least two major thresholds occurring during Charlemagne's career alone (one toward conquest, one away from conquest and toward domestic affairs). So yes, people had long-term aspirations, but these aspirations weren't consistent, and to describe them as a political 'Grand Strategy' risks obscuring the ways in which early medieval peoples understood and acted in their world.

Bachrach and a selection of further reading:

Bernard S. Bachrach, Early Carolingian Warfare: Prelude to Empire (Philadelphia, 2001).
Guy Halsall, review of Early Carolingian Warfare. (link courtesy of /u/Rittermeister)
Jennifer R. Davis, Charlemagne’s Practice of Empire (Cambridge, 2015).
Rosamond McKitterick, ed., Carolingian Culture: Emulation and Innovation (Cambridge, 1994). (especially the articles by Brown, "The Carolingian Renaissance"; Innes and McKitterick, "The Writing of History"; and Nelson, "Kingship and Empire in the Carolingian World")
Rosamond McKitterick, "The Illusion of Royal Power in the Carolingian Annals," English Historical Review 115,460 (2000), 1-20.
Rosamond McKitterick, History and Memory in the Carolingian World (Cambridge, 2004).