Honestly, you know what they could do is a riff on the Gibson draft of Alien III. It would require a semi-significant rewrite, but it would allow for a "B" line in the series without undoing Alien 3 or A:R.
USS Sulaco is found drifting through space, recovered, and taken to Anchorpoint. It apparently drifted through the UPP faction's territory.
Ship is deserted, signs of a fire, damage to major systems, and alien genetic material is recovered on board, and cultivated in the lab.
You could retain connections to Aliens in an Alien Isolation style. Have some kind of a log delivered via voice over from Hicks/Ripley. Since the script originally implied that UPP had similiar but less advanced tech (IE Soviet Union...In SPAAAACE) it would be a way to work in Working Joe type droids or something.