I'd like to add my voice to the chorus. I think this would be a good use for engineering divisions as well. I'd also like to see your option 2 merged in but with automated mines added. I find the idea of making an alien shipyard work after however many thousands of years a little implausible.
Sounds like the consensus is to use an engineering division to restore alien installations, probably using the xenology bonus of its commander to modify the chance of a successful recovery. The trick will be finding a way to differentiate between engineers restoring alien facilities and engineers involved in construction but I can probably do that with a flag on the Ground Forces window.
Now as to what can actually be restored. I don't think anyone would have a problem with minerals, fuel, infrastructure and automated mines. Probably missiles are OK too. A commercial spaceport is OK as that would be like capturing an airbase but I agree that intact shipyards are probably too much. Restoring tracking stations and mass drivers might be possible as their function is relatively simple and therefore and the same applies to terraforming installations. Even maintenance facilities could be thought of as a port so they could be recoverable. The big question is over construction/ordnance/fighter factories, fuel refineries and research faciltiies.
A further couple of points first though. I think everyone has a different idea of how old the ruins are. If our own civilization fell into ruin and was discovered thousands of years later then it's likely not very much at all would be recoverable. if it was discovered a hundred years later, then alien visitors could probably recover quite a lot. I have never really defined how old the Precursors are so perhaps I need to do that before we can create a reasonable solution. We can take a realistic approach based on the age of the galaxy and the possible lifetime of technological civilizations, in which case any ruins would likely be millions of years old. Or we could take a Star Trek, Babylon V or even Starfire approach where most races are relatively even in technical development (with the occasional exceptions such as the Organians or Vorlons). In the latter case, the ruins may only be centuries or even just decades old, which would also make the robotic ships more believable too. In fact, Aurora assumes that situation already becaue the NPRs are relatively even in tech, which indicates they probably evolved on a similar timescale to humans.
How about this scenario? The Precursors are an ancient race that decided to eliminate all other intelligent species in the galaxy. Reluctant to leave their planet, they built their robotic ships to do their bidding and sent them out into space on that mission, preventing any space-capable civilization from expanding into the universe and beocming a threat. The precursor ships found in orbit are therefore the ships that actually caused the destruction of the population below and the ruins are from a wide variety of different species. A century ago, some disaster befell the precursor homeworld (plague, rogue ships, etc.) and it was laid waste. The robotic ships out in the galaxy had no one to command them so they held their positions, continuing with their last orders to destroy any intelligent species. In the century since the demise of the precursors, intelligent species have finally been able to expand into space without interference and that is why they are all relatively equal in terms of tech and why the ruins are not very old.
An alternative scenario is that the precursor civilization was benign and widespread and had brought many other species into a huge pan-galactic empire. As new species demonstrated an ability to travel between stars, they were contacted and became part of the precursor domain (a benevolent Hre'Drak). A century ago, a virulent and deadly plague spread throughout the galaxy, completly wiping out most of the precursor species and sending the survivors into mini dark ages but leaving much of the planetary facilities intact. Those desolate worlds are now the ruin sites and the plague explains why the structures are relatively intact (maybe we call them 'abandoned worlds' instead of 'ruins' in the case of this scenario). Some warship commanders, realising their imminent demise, put their ships on automatic with orders to defend their homeworlds.
Either of those scenarios could provide a reason for relatively recent ruins with a good chance of restoring installations, at least from a physical perspective. I guess the real trick would be deceiphering the alien language and control systems so you could operate them. Assuming the ruins are from multiple species, perhaps each ruin is checked to see if it matches a species from another ruin or is a new 'dead' species. A new research project could be generated for each dead species that would allow you to understand their language and control systems. Completing that research would be necessary before you could restore installations. Or better still, the Xenology Team is retained but with a new mission. Before engineers can begin restoring installations, the Xenology Team must study those ruins until they learn enough about the alien species to permit recovery to begin. The Xenology team becomes the brains that learns to understand the aliens then the engineer divisions can get to work on the recovery. The length of time it would take the Xenology Team would be randomised and unknown to the player until it was completed, but it would depend heavily on the team skill. How does that sound? If a second ruin site from the same alien race is found, the Xenology Team would be unnecesary.
Steve