I have excellent credit and good paying job approval will not be a problem. 

LLC Transfer & the Due on Sale Clause•HELOC: If you take out a Home Equity Line of Credit (HELOC) on your rental, most lenders require the property to stay in your name.

Definitely a question for a tax attorney/accountant, especially with the dollar amounts involved. 

DM me, and I will send you contacts for attorneys, lenders, and accountants they have previously used.

If you have equity and decent credit, a conventional Fannie Mae HomeStyle (or the Freddie Mac version) would likely be the better option instead of an FHA 203k loan (which will require a 3rd party HUD consultant to oversee the deal in addition to having the contractor involved). 

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

.- They add 15% margin to the repair costs.They don't have good accounting system to get good clarity on monthly transactions like rental payments, expenses, etc.  

I own the property free and clear and i use the equity as part of my business line of credit.

Full credit/background check:  Look for missed payments, and any theft is always a no go.2.)

[1]    You might want to think about opening 2 FDIC insured savings accounts that have no fees.