Hi Math,
I hope your New Year is off to a great start! What you’ve described is definitely possible though it might require the use of additional plugins to bridge the gap. I’d check out plugins like User Role Editor and Theme My Login, though I’m not 100% certain the best ones to use for your situation.
I’ve personally set up a site similar to what you’ve described using Gravity Forms and a few of it’s Add-Ons. Lastly, try searching the forums to see if you can find any specific examples of users doing the same thing you’re looking to accomplish.
Best of luck and let me know if you have any more questions. Cheers!