I agree that the UP resolutions seem too random. They're often more of a surprise than a real strategic option (wait, why are we voting on this?). I think it would be interesting to have an option for a strong UP (or maybe this could be a resolution people could vote on -- "strengthen the powers of the UP? Y/N"). For people who really hate the UP, tthis could be a map option.
Also, maybe there should be a list of potential laws that can be passed. Players with high influence should be able to set the agenda. Maybe the top 2 (or 3) influence players can pick a motion they want to vote on.
I was also thinking that maybe there should be required UP dues (like UN dues... 5% a year?). And every year someone gets voted as UP secretary-general. Being the UP secretary-general would actually get you access to that UP income (or something). Maybe find a way to tie that to tourism or something. Basically, you get the benefits of galactic bureaucratic largess. Or every year, the UP secretary general can build one special UP building (a UP research institute, or a UP special economic zone, or a UP manufacturing center, whatever). Just one unique building... ok, I'm just brainstorming. Just trying to think of ways that players would really care about accumulating influence to actually try to control the UP.
I guess the idea is that influence and diplomacy could be even more important, and that would give players another variation on the diplomatic strategy. You make alliances, but you also squeeze out players you don't like by obstructing them with laws that happen to promote peace and justice (i.e. favor you).