Worse case, if you do the rent decrease, is that you have a non-cash flowing property/rentals below market rent as well as you have tenants who expect their rent to be lowered at every inconvience.

One-time, non-refundable, and Re-Key Fee $125.

Since my private lender did not require a down payment, this approach would work well.

How do lenders usually approach transactions involving tenancy in common? 

And I am talking non trivial. 

To use our remaining VA entitlement and put down as little as possible (without paying PMI), and quoted 5.375% interest by Meritage's preferred lender, our estimated cash to close is $72,000. 

Definitely a question for a lender however this seems like a good option given your capital situation. 

Call the local municipality where your rental property is located and ask if they have a list of certified local contractors or see the attached link for a list of NJ Certified Lead Evaluators...https://www.nj.gov/dca/divisions/codes/publications/pdf_lead...

These properties are very low value for most lenders.

I would recommend building up your cash up first as most hard money lenders will only allow 70-75% LTV for a first timer.