I like the idea of Ripley landing in a kind of space monastery better. Maybe the wooden planet bit is over the top, but seriously, 'rapists, murderers and child molestors' don't make the best protagonists for an Alien movie.
Hicks and Newt surviving the crash woule be also much better I think, what if maybe Hicks was mutilated, for example lost an arm or leg, and later on that could be a source of major problems. Hicks would be quite immoblizied for the most of the movie. Looking at it again though, he was already in quite a bad state at the end of 'Aliens'. Also, I think there could be interesting differences and conflicts between peace-loving monks and the soldier (and Ripley, too), different mentalities, approach to the alien problem, etc.
Ripley dying and sacrificing herself at the end is a great ending I think, don't know about Hicks, but I would like to leave Newt alive, as "the promise of new life contained in each death" as Dillon has put it. By the way, the scene of the cremation/alien being born is one of the most beautiful in the whole saga. That's my favourite moment in Fincher's movie. If I could, I'd leave it intact.
I also think that one of the earlier ideas of killing the Alien, I mean drowning it in liquid glass (the monks could be some kind of artistic glass crafters, dunno) would also be more interesting. Imagine the glass after hardening, and the Alien trapped inside, like a mosquito in the amber...
The whole running/closing door scene is too B-movie for me to leave, I don't like this scene and it fits better a Jurassic Park kinda adventure-thriller movie, not a grime, dark horror that the Alien should be.
As for the audiovisual side, this is one of the greatest assets of Alien 3 and I don't think we need to change this. That's all the changes I'd make, for now.