Mary,
I am no longer employed with UI Extension, but I would suggest you consult with an arborist about whether pruning the trees is a logical next step. Extension staff and Master Gardeners don't routinely make house calls. Here is a good link for finding a certified arborist: https://www.treesaregood.org/findanarborist/findanarborist Many will give an assessment/estimate free of charge. You also have a city arborist, Kevin Sanderson (ktsanderson@urbanaillinois.us). I don't know what the policies are in Urbana, but maybe he can offer some advice.
You're absolutely correct that if there is a lot of damage to existing branches, the trees will likely look lopsided. It's hard to say for certain whether they are worth saving without a picture, and honestly, without seeing the tree in person to really assess what you're dealing with. Hopefully those resources I shared can help you figure out next steps. Good Luck! -Jennifer Nelson