I was digging around in a Wikipedia rabbit-hole and ended reading up on part of Tacitus's Annals, as one does. I started reading his account of the Great Fire of Rome, and its relation to his mention of the crucifixion of Jesus. But while reading I came across chapter 42 of book 15 which felt oddly out of place being between those two events.
The chapter starts by discussing how Nero took advantage of the fire and a desolate Rome to build an extravagant palace. Tacitus then lists the names of a pair of builders for the project and their skills as engineers. Afterwards however, Tacitus casually brings up a canal proposed by the same pair of engineers to construct a waterway from "the lake Avernus to the mouths of the Tiber-". He then describes how the local terrain would cause difficulty with the plan. Even so Nero had apparently "[dug] through the nearest hills to Avernus, and there still remain[s] the traces of his disappointed hope."
After this chapter there is no mention of this canal or the two engineers mentioned. Tacitus simply continues on how Nero cleaned the rubble, implemented new building codes, and Nero's persecution of the Christians as blame for the fire.
What would the reason be then to have such an expensive and difficult to build canal that would seemingly have no purpose connecting two bodies of water that already have a connection to the sea?
Also I spent some time measuring out what a possible route^(*(one that has no real basis in reality just one I created on a whim based off of the text)) could have been so may as well share it here:
As the crow flies the distance from the mouth of the river Tiber and lake Avernus is just over 180km, but by drawing a more dynamic line (following flat-ish terrain as much as possible) the distance is more like 200km. The canal would also need to rise and fall by roughly 280m and 150m for the Aurunci Mountains and the temple of Jupiter at Anxur respectfully.
It is usually termed the fossa Neronis. (fossa is Latin for "ditch" or "trench", from the verb fodiō, fodere, fōdī, fossum "dig up, excavate), or the fossa del Castagno in Italian sometimes. Another source that mentions it is the biographer Suetonius, Nero 31:
He also began . . . a canal from [Lake] Avernus [at the town of Puteoli] all the way to Ostia, to enable the journey to be made by ship yet not by sea; its length was to be a hundred and sixty [Roman] miles and its breadth sufficient to allows ships with five banks of oars to pass each other. For the execution of these projects he had given orders that the prisoners all over the empire should be transported to Italy, and that those who were convicted even of capital crimes should be punished in no other way than by sentence to this work.
The project was at least started and possibly progressed from 64 to 69 CE, as Johannowsky showed. As the sources explain, the project was meant to better facilitate the delivery of grain to the capital. The stretch from the Bay of Naples up to the port facilities at the mouth of the Tiber was treacherous, and we get the impression that the port facilities themselves were often dangerous to shipping due to flooding and storms. The main issue was the bottleneck: the facilities at the mouth of the Tiber were never sufficient to accommodate the vast amount of grain shipping required to supply the capital, and they weren't suitable for the big Alexandrian transports at all. Those ships had to offload cargo at Puteoli, in the Bay of Naples, and then the cargo had to be moved up the coast to the Tiber via smaller ships. This resulted, we understand, in ships stacking up at anchor at Ostia precariously. Claudius had created a new port north of the mouth of the river, but it was (we surmise) still not sufficient; this was not "solved" until Trajan's upgrades to the Portus (now largely underneath the Fiumicino airport grounds). Nero's engineers had sought to eliminate the sea route entirely and use the fossa to transport grain safely from the Campanian agricultural hub at Puteoli, thus cutting costs—both the costs of battling the sea and also the enormous costs of transporting Campanian and imported grain to the capital overland. The emperor Domitian would later build a road to further lessen the impact of this overland route. In essence, the excellent and safe harbors at the Bay of Naples could have been used as a massive staging area for off-loading the grain, which could then be sorted and transported via the fossa without having to worry about storms getting to the stockpiles before they could be brought ashore. It's a great idea and it's the kind of big engineering that the Romans were so good at. It is also an excellent example when anyone brings up geographical determinism (common on the sub here): Rome is completely ill-suited to have existed where it did, and getting enough supplies to support a million+ people there was a logistical nightmare. By the way: even if the fossa had been completed, the grain would still only get to Ostia. From there, it would have to be put on the barges and dragged up the Tiber to the city itself. I think Tacitus' appraisal of the project is misguided, and he of course had an agenda to ascribe the project to Nero's megalomania. Modern studies also often point out the enormous cost of the project's creation, the cost of maintaining the long waterway, of infrastructure along it, etc etc. I think if a modern civil engineer were to consider all the factors of the project in ancient terms with ancient technology (not least of which was "free" labor), she or he would probably conclude that in the long run, over the course of several centuries, it would have been well worth the cost in terms of logistics, not to mention the political expediency in somewhat relieving the constant headache which was the threatened grain supply.
Some traces of the work have been known since the early 20th century, mostly at the southern end. There are some fundamental disagreements as to how it might have run exactly, and many have done your mapping exercise. One problem is that the ancient terrain has changed quite a bit in the intervening two millennia. There are a couple of reliable write-ups of the fossa available online, including one by Johannowski here. It's in Italian, but google translate can do a decent job on it I'm sure. Another discussion here, also in Italian.