We had one case where the sale was court contested and cost us $45,000 in legal fees and after 9 years of Depositions, Interrogatories, etc, we still had not gone before the judge. 

I would suggest adding a pet addendum or modifying the page of the lease that refers to pets.Having the changes initialed and dated by all parties and reflect the changes to accounting "pet deposit" or additional deposit.

First question is to ask them if they're approved today can they pay the deposit today?

If you are pulling a HELOC or taking family money, leveraging credit cards, using personal savings it took you years to accumulate, whatever the source of money is - unless the source is endless - start small. 

My understanding is that so long as they confirm that they're moved out and give me the keys, I'm well within my rights to just have a junk remover / trash company take whatever was not there to begin with, and deduct that from the security deposit?

When I self-managed C Class properties, I would put the requirements for tenancy in the rental listing (3x rent in income, 1-month security deposit, criminal check, etc.), and then when the potential tenants called in, I would speak to them for a few minutes, explain the requirements, get some sort of verbal confirmation on some or all of the requirements, and then invite them to different showing times I had set up.

This is in theory a sunk cost for the tenants, in some cities in Washington you have to apply the application fee to the "move in costs" which cannot exceed the cost of 1 month's rent and including the security deposit fee.

If I was a landlord I would ask for two months deposit plus first months rent upfront to show your commitment, then rent to start 4 months from lease signature.  3% escalations a year and an option to renew for another 10 years assuming all rents were paid on time.  4 months puts the pressure on you to work full time to get the place where you need it to be. 

It would be endless debate.Florida/TX may crash while CA going to all time high too in case of real estate valuation.

(and realistically a different fully qualified applicant will be given the lease while the first person tries to obtain additional documents)My lease allows for a small monthly pet fee, a modest non-refundable pet deposit, and verbiage that if they lie about the status of a service animal, that they will be charged an additional large fee for lying.