A typical BRRRR in DC creates $200k in equity.

You either have to earn extra money via sweat equity (working as your own PM or do the renovation work), or you have to be ok with a negative cash flow.  

As mentioned by @Chris Mason, Bridge Loans: These short-term loans can provide immediate financing until more traditional financing becomes available or until the property stabilizes and becomes more attractive to lenders.Interest rates and stipulations may be a pain.Out of the box here and requires a few more research, SBA Loans: Small Business Administration loans can be an option, especially the SBA 7(a) loan program, which can be used for hotel acquisitions.I heard someone  mention - Mezzanine Financing: it involves a combination of debt and equity financing, which might appeal to some investors looking for higher returns.

I've purchased homes for my own residence, but never an investment.

You could structure a profit split or equity share where you handle project execution while they bring the funding.

That sale should qualify for the $500,000 sale of personal residence exemption for tax purposes.

Their plan is to raise rents (on the poor remaining souls, improve infrastructure and exert some sweat equity. 

Really expedites the time it takes to reach FI when you can completely eliminate your housing payment and get into multis for such little down and start building equity/cash flow with each one.

I was actually considering doing a shorter mortgage term to gain equity on the property faster.

Do you have equity?