The listing has cash or conventional loans only which eliminate at least 1/2 of your buyer pool.

Why not look at a fixed 1st mortgage followed by a small 2nd mortgage to eliminate the MI all together.

Debt or equity?

It also eliminates potential liability for the title company, who can reasonably rely upon the docs ... unless there are some other material facts not being shared here.

Debt is not an indicator of what your tax liability would be.And yes, the way to alleviate that is to add a number to the BRRRR strategy - 1031. 

The presumption here is ZERO debt whatsoever.

The last thing that comes to mind is a hybrid debt instrument but that could get a little tricky.You aren't going to get any legal advice on here so if you are legitimately concerned you will want to talk to an attorney about your specific concerns and they will let you know if you can structure around it.

@Clayton Hutton  A simpler way to do it may be to bring your friends on as debt investors and just give them a fixed return for the use of their money (more like a private money lender) instead of making them equity partners and giving them some percentage of the deal. 

They lend at higher rates but are also willing to fund deals for borrowers with poor credit, income, debt levels and experience. 

When a foreclosing Lender takes a property back at the mtg foreclosure auction, state law dictates the lender gets a set discount on any past hoa debts....the l Nader only has to pay either 1% of the original loan amount or 12months of dues, whichever is less..I assume though that maybe you are talking about hoa dues During the time the bank owned it?