If no one with more expertise responds with a better suggestion, I recommend you start with finding out what some local banks/credit unions have to offer.Good luck

Also, I would need to know who’s credit and guarantee is involved as I would check the applicants background before approving an application.

My current credit score is 650.

I keep hearing that I should keep my first loan on the books for 5 years...My question is; Will it matter (as to building credit) weather or not it’s the same loan?

We have good credit (by any standard) and a decent bank account (by college standards) but not enough to put down the standard 15-25% most HML and private lenders prefer.

My current credit score is 650. 

Before you continue down the modification path much further I'd get in touch with someone who specializes in garage conversions or ADUs and get an approximate price and timeline and run the numbers again, it seems like you may be underestimating the cost, time, and difficulty of a project like this.

1. most banks/ credit unions are telling me I have to wait a minimum of 6 months after closing before I can get a cash out refi..

You should do whatever refreshes your cash/credit pool the fastest so you can move on to the next deal.

With current LTV, the credit union says we have been approved for approx $48K.