If you are charging market rent, the rent you will lose for that 1 week of occupancy would afford you the ability to rent a comparable property on the market without the need for any of this kind of nonsense. 

You will probably lose money even if you rent it for $1,800.

There’s also the added pressure of not wanting to lose out on a property, which makes it harder to justify putting up serious money before going under contract.On the other hand, if such a system were standard, it might push sellers to be more transparent from the start, so buyers know exactly what they’re walking into.

Any recommendations or suggestions for ways to negotiate this (and not lose our earnest money)?

If you lose to a different offer, it is what it is.

So you would need to look into is losing about $700 a month is worth it and can you deal with that for a period of time.

Fast solutions have slow problems, tie yourself up in getting cute and the reward is you get a property and risk is you lose it all.

Owning a lot of cheap properties with crappy tenants is a great way to lose money.

Better to own a few quality properties than a bunch of crapboxes that end up damaged and vacant and eventually lose money.

The agreements I've seen basically say you are guaranteed nothing, you could lose all your money, you might not be paid on time or ever, you can't rely on any representation made by the GP, you have no control over the operation and other terms and disclaimers to that effect.