Regarding the balloon, does your hard money note have options for an extension built-in? Some do, some don't. If it looks like you won't be able to payoff before the balloon happens, then you should speak with the lender ASAP and let them know you're either trying to sell or refi (whichever is the case). You may be in a better position to discuss/negotiate an extension now as opposed to after a default, but not necessarily depending on the motivations and values of the lender.
Sitting on it seems like the worst option... either list it or refi/rent it ASAP. As for the >10 days concern, if it's not listed you've essentially tagged it yourself and have a near zero chance of selling.
Personally, I'm not a fan of rehabbing. It's been a while, but I've done a number of "prehabs" where we just clean the place up (cleaning crew, trash disposal, light landscaping) and put it on the market. Have sold to a variety of people, including other investors (landlords and rehabbers) and owner occupants that have some fixup skills or are just looking for a "deal".
-Drew