Need some help /Advice surrounding a Tenant that caused water Damage

[Gabe N.]

Hi 

I have a single family home rental property in Texas.
Their lease is about to expire in 30 days. 14 days after my My tenant gave his 60 day notice, the tenant overfilled the kitchen sink and flooded a portion of the house. He took responsibility and said that he will cover the damages. The same day that this happened he hired and paid for a water removal/restoration company that came and brought some fans and a dehumidifier going for about a week. The tenant paid for this service and told me that he will coverall of the water damages. As time went by we learned that the kitchen cabinets might be damaged and most company's prefer to tear everything out and do a full replace instead of doing the cabinet repair. The tenant proposed that he will pay for the insurance deductible in order to cover the damages.

My concerns are that given my previous interactions with him, he doesn't fulfil his promises and kind of hinted in an indirect way that i can just keep his deposit.  

I don't want to drag this out so I am trying to avoid going through a full kitchen remodel and avoid going through insurance since the house will not be occupied for several months.

For reference most of the quotes that I have received are over 10k.

How much should i charge him for the damage (my insurance deductible or the actual amount I will pay to do the work)?
What is the best course of action that i can take in order to ensure that i get reimbursed or paid for the damage?
What would a professional management company do in this type of scenario?

Thanks in Advance
-Gabe