With your background in the Air Force, MBA, and construction, you're in a great position to launch a real estate venture.

Does anyone have experience of setting up a STR while in the same position? 

I do want liquidity to invest elsewhere which is why I'd like the cash back from the reno ASAP, but I don't need liquidity equal to the value of the house--just the basement build-out, if possible.With option #3--how do you "cash out immediately"?

Youre with WAY too many options and decisions at one gulp.

How do others manage to create positive cash flow from MF properties with debt?

I'm happy to chat about your options to see if we can get you out of this mess. 

Have 3 loans to refinance in the next few years and DSCR's are added to the option list.

After 4-5-6 years then maybe roll them up into a small mulitfamily.Another option if you have the credit and some capital is to buy a 4 unit as owner/occupied and live in one and rent the other 3. 

My agent is saying that we are unable to split the contract that way (or reduce the purchase price), so I'm trying to figure out options.

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.