Well, you're right that invasiveness can vary from place to place. Even within the area here, there are some places where weeping cherry has naturalized pretty agressively, many others where it doesn't really at all. Like Siberian elm, I know many places in NM it's crazy, I thought it was in CO also? But not really at all many other places. Paulownia, on the other hand, rivals Ailanthus sometimes in the range of conditions it can grow in and spread. I personally don't know about Iowa, but I would be extremely cautious. Each tree contains hundreds of pods, each pod contains hundreds of airborne seeds. I've seen them pop up in the Smokies miles and miles deep in the forest from the nearest population.
But I know you said ignoring the possibility of invasiveness, I just have a hard time with that. I know what you mean when you say what might be listed someplace might not be a real reflection. I think of most invasives as biological pollution. They're just plants doing what plants do, can't blame them, and it is humans who screw things up by moving stuff around so much, but I think it's better to limit it than ignore it. Just because they're not diseases or insects like chesnut blight or HWA or whatever, doesn't mean they don't do damage. Not to be preachy or anything.
As far as their properties, the growth is incredibly fast, pretty coarse with very fat twigs, and the wood is light and brittle, alot like Ailanthus. We've clogged a chipper just chipping limbs with seed pods, they are so gummy and wet. They're pretty messy, but the flowers are pretty and unusual. The form is okay, fairly open, loose, decurrent branching. Something comparable but I think probably much better might be Catalpa, probably northern up there, they're pretty tough even in plains situations. A bit messy also, and they're not native there, either. The leaves can get pretty beaten by hail if it hits. I'm not sure how invasive they might be there.