Perhaps a nice 1950's built bungalow.Always hire a 3rd party property inspector to give you an unbiased feel for the home.

Set up an escrow account and all parties are protected.

The tricky part is that I am a non-resident living outside of the US (so basically no ties to the US other than my 50% stake in these two properties).

Parties over.

For may part, I am not going to charge a late fee, but make it clear to the tenants that eventually the rent will need paid, just as my owners have a mortgage to pay.  

Perhaps a nice 1950's built bungalow.Always hire a 3rd party property inspector to give you an unbiased feel for the home.

Both parties agree on condition up front, and both agree on condition at end, you are less likely to get pushback if you withhold all or part of the deposit.In your situation, no deposit does not technically mean no liability for damages, but obviously harder to assess, particularly if you don't have any type of documentation of the condition before tenant moved in. 

Just keep the deal together and close as soon as it’s possible, neither party should have a problem with that given the situation.Best of luck! 

Clearly a quandary for which there aren't a lot of viable solutions.Several steps can be taken to help create an acceptable situation for both parties.

A system may not be fair for all parties equally, but it still could be the best overall solution.