Yeah, so, I had the spots available on a planet;
I qued up and completed all four research tiers in one shot;
The titan button stayed grey, and clicking it told me I needed a capital ship factory.
Had the capital ship factory; actually, though, it was destroyed once, but I rebuilt it.
I don't know if I was rebel or loyalist, because I just let it randomize.
I'll upload a save-game, if it would help.
Thanks! Keep up the good work!
(...and we'll stay on friendly terms...)