So, I invested in VictorPest Rat Zapper (Victor is the company that makes the original snap mouse traps) It runs on batteries and it zaps the rats with electric voltage, they die instantly.

They say that the contract is at will and can be terminated at any time for any reason. 

In the absence of title insurance--which is not available for a quitclaim deed--the person receiving the quitclaim deed has no legal recourse because the deed itself states that only the interest of the grantor, if any interest exists, is conveyed.Whether title insurance terminates by transferring real property depends on the type of policy, and how “insured” is defined in the policy.

Would this be enough for others to want to terminate the relationship or would you still let him manage it as a rental?

Make sure it explicitly explains the process for termination if you are unhappy with their services, but especially if they violate the terms of your agreement.3.

I would have fired long ago, but I signed a year contract with them and have a $1k early termination fee.

@Anthony Wick haters gonna hate.I use a one-year lease with termination fees.

(iv) If Buyer is unable to obtain Loan Approval after the exercise of diligent effort, then at any time prior to expiration of the Loan Approval Period, Buyer may provide written notice to Seller stating that Buyer has been unable to obtain Loan Approval and has elected to either:(1) waive Loan Approval, in which event this Contract will continue as if Loan Approval had been obtained; or (2) terminate this Contract.

In your scenario above, the lease has been broken and hence cancelled/terminated, not expired. 

If their previous lease was long term, you need to honor the terms of the previous lease until it expires OR negotiate with the tenant to mutually terminate the previous agreement and enter into yours.