I am on a team and we regularly host meet-ups in the Denver area.

It shouldn't take much to clean and you can rent it quickly.If they don't agree, then they will remain responsible for rent, utilities, or other charges until a replacement tenant takes over for the same terms.

Snow clean up? 

They cleaned the house and did a decent job. 

Typically, you will have some repaint, carpet cleaning or replacement, etc in each turn over.  

When auction.com had live auctions in 2008 to 2010 the auctioneer guaranteed the titles would be clean and free of liens and encumbrances, but today the auctioneers will not give any clue in regards to a clean title.

Use the deposit to handle cleaning and repairs, then refund the remainder.

I want to write the owners a letter (I'm 3 hours away) explaining the situation and asking them to at least pay the legal and recording fees for getting it cleaned up. 

Toilet paper, cleaning supplies, coffee, towels and sheets, laundry detergent, etc.  

We are in a great cash position to be able to put a good down payment, but conversations I've had about getting a mortgage have turned negative real quick just because I don't have a "regular" job.