Wow, thanks for the feedback everyone.
Are the flowers and leaves safe for parrots (or, rather, Pionus)? Not that I'd go around purposefully
feeding them to my bird, but I'd just like to know since parrots chew just about
everything.
@Andie: How quickly would you say the trees "recover" from you cutting the branches off? Would you say the tree regrows fairly quickly? Any specific timespan you can think of? While I don't think I would have to cut off a lot of branches over a short period of time, I'd like to get an idea what could safely be cut off a tree (after all, I'd love for it to be sustainable).
Thanks again for all the info (keep it coming!), your first-hand experience is leaps better than the online articles I've come across.
Edit: I would love to get a hanging gym...it would answer my "where on earth am I going to
put all this stuff?" questions. :P But alas, not only is it still too pricey for a "disposable" play gym, but I can't hang things from the ceiling.