This may be the best of both worlds scenario, some income and some recapture of equity.

What would be some common pitfalls in either transaction?

But, I am still confused where a refi comes in to play, or doesn't, in your hold scenario.  

(Another option to the above scenario is to instead have the LLC lend my father money to complete the rehab so all the repairs are made in his name...but then the LLC would get no tax deductions on the rehab, plus my father would wind up paying interest on the loan and the LLC would incur taxable income on the interest of the loan as well.)I've said a lot here, but It would be greatly appreciated if anyone can give me advice on the best strategy to pursue...Thanks!

It's very common to have a credit card used during a free-trial sign up.

It is very common in this space to have the terms changed right before closing. 

As a junior in possession they may work with you.  86k is not enough to do a BK over that would really hurt you going forward. worse that comes out of it is you know their position. its possible though that the property will bid higher than the 600k . if it goes to sale make sure you attend and watch the action very closely make sure bidders that qualify checks are not talking to each other and making side deals so the property only goes for minimum bid and you get nothing.. this is called colluding to stymie open bidding and in some markets it quite common.

Software is a common question on BiggerPockets.

My advice here would be exactly the scenario I did last year. 

Knowing more specifics about your scenario and goal, will help provide a more customize approach for you.