I suspect your Tenants are abusing the cooling system and not ventilating the home properly.you could potentially fix this with a dehumidifier to suck the moisture out of the air.My response would be exactly what Greg wrote.

@Ryan Jackson, if a military member gets deployed and clauses out they certainly are not abusing the system at all. 

I appreciate the experiences you guys have shared.To sum it up, it seems the major concerns include making sure the work gets done before actually paying the person or deducting it from the rent (also something that would need to be done with a regular contractor) and proper relationship maintenance, ie keeping the tenant relationship separate from the contractor relationship so it isn't abused. 

Jerry I hear you, but from my experience the system is a disingenuous system because explain to my how the bank can deny a person a loan to purchase a home for him and his family which the payments on would be lower then his rent payment, but that same bank approves that same person for a car loan that he can't afford along with a few high interest credit cards.

I love my job and at the same time, it's pure abuse to my body.

Muddling around trying to avoid a premium increase could get you deeper in to trouble, or open a door for a company to deny the claim (e.g. 

.$850 and the tenant sends only $500 will the payment get denied or will the lesser amount go through?

Ask for the comps again, if you are still denied it may be worth it to find an agent that has you best interest in mind.I'm a new agent and looking for my first investment property.  

Quote from @Denis Ponder: For those who MTR, what revenue multiplier makes sense to you for the additional work and cost of an MTR over an LTR?

This is due to the outrageous abuses sellers used to swindle buyers out of properties they made payments on for 10,20 even 30 years.