I MAYBE could understand if they just hadn't gotten around to having automated credit card tracking like every other accounting software on the planet, but to not even have the option to track them manually is ludicrous.  

It's not worth hiring a lawyer but as you suggested, small claims court may be an option IF you hired them in your personal capacity OR if your jurisdiction allows LLC owners to go to small claims and represent the LLC in court (many, most?

Feel free to PM me if you'd like to talk options.

Another option would be working with private lenders to see if they're open to your idea should you need additional funding. 

You can tell that the lender isn't granting this extension under the provisions of the loan's 1-year extension options.  

Once I gave them the online option, however, and the bank didn't deliver one tenant's check causing a late fee, they've all used the online option.

I suggest your next lease have such a clause and that you make sure you can find the lease (but i have also somehow lost a lease recently).For where you are now, without a signed copy of lease i believe your options are limited.  

If you’re leaning toward an LLC, I can recommend some local options to help set it up.

As already mentioned, he wouldn't be able to use rent from roommates to help qualify but based on the numbers you shared there should be a VA option available considering how much flexibility there is. 

Happy to connect and talk about options.