Despite what I got on my timer, I'm thinking I need to err on the conservative side and say 4:03, as I think I ended it a little bit early (timing on my highlight gave about 4:02, but +1 for caution). I'll take my recording and do a frame analysis later.

Here's the strategy:

Pick silicoids for their extreme early game production bonuses (no waste) and for not needing any research to colonize planets. Research range 5 fuel cells and fusion bombs immediately. Warp 2 engines would be nice too but I didn't get that this time. Build excess colony ships, get in range of their worlds, build as many ships as I need to win. Profit!

I suspect that Bulrathi invasion might still be a viable strategy, if I had one world dedicated to repopulation and could conceivably send enough to conquer.