Is there a better way to structure this deal besides proportionally splitting the profit from refinancing (and/or eventually selling) and the rent (which we'd be paying)?

Eventually paid, but pretty sure the jet ski was paid with rent.)

They will evaluate the property, eventual costs with repairs, etc - depending on the service you asks and their fees are about 250 EUR per report.

Though my property management company eventually took care of the eviction proceedings and repaired the property to prepare for a new tenant, I feel they were negligent in their duties.

This will crash and burn eventually when real estate (temporarily) resets itself and reprices the assets down. 

I am happy to accrue the $500 / month interest so long as they come through and eventually pay, but they have paid in the past, so I am hopeful that they will do so in the future.

The way you present things I can see this occurring eventually.  

Eventually, Class A property values increased to the point that even increasing rents didn't allow them to cashflow upon purchase.So, the flood of new investors switched to buying Class B properties.

Eventually, you will be sued and end up in court.

You can try and fight it but does not mean you will be successfulI would also be curious to see what your property insurance looks likeFor me this is just another example that home prices are gonna eventually have to soften as between taxes, insurance and Interest rates home affordability is very challenging