It really based on you but if you are familiar with running comps and understand the market value of your home than you could run the risk of losing money.

Will they lose their ability to deduct bonus depreciation against their regular 9-5 income for all future years?

This bill is misleading as it states it's to help the individual  losing the house by giving them the equity. 

You also will not be able to see the house and no one should buy sight unseen without a history of doing it.If you are talking about Auction dot com or Xome or Hubzu, those come with a buyer's premium on top of the sale price between 5-10% and often have ghost bidders in the system so you will see it keep getting reset to hit a higher bottom.As a new(er) investor, auctions are where you go to lose money and take on excessive risk.

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.