If I create the LLC and vest title in it to the HML's liking, how and when would I transfer ownership of the property to my Individual name to be eligible for a conventional refi?

I would ask your lender before accepting any money because it may have to be transferred in a certain way to appease the lender. 

They are welcome to submit a complete application if they wish to remain and sign a new agreement with our terms, which may, or may not, be different from current terms, depending on our findings of condition, current market conditions, and their credit worthiness.Be sure you are getting the security deposits transferred to you at closing, and confirmation of rents/deposit with estoppel.

On Hamilton County utilities since the city wouldn't let me transfer it over to tenant.

The assessed value is initially established when the property transfers so, especially if it was purchased some time ago, the assessed value has no correlation to today's market value.

As long as we can document the terms, verify that Uncle Bob is not a party to the sale, and verify the transfer of funds.  

If Texas requires a deed to be recorded to transfer title from a deceased's estate, then you may need to take some curative actions to clear up title.

Title examinationRealty Transfer FeeRealty Transfer Fee TaxAs far as I am concerned, what other additional costs should a buyer pay beyond the title search and transfer tax?

My lawyer transferred the deed of my rental house to my LLC. 

We monitor the progress as a percentage of the total tasks and pay for the progress made by ACH transfer every Friday.