I think we are going to stop paying them and cut our losses...It will ruin our credit for over 7 years,
Before you decide to do that there are other considerations.
The TX statute of limitations is 4 years. That means, once you default, the creditor has 4 years to file a lawsuit for any balance of the loan and any unpaid fees. Once the creditor sues, it's virtually guaranteed to get a judgment unless you file bankruptcy. Once the creditor gets a judgment, the judgment is enforceable for 10 years (possibly renewable) and allows the creditor to levy bank accounts and attach non-exempt assets. Fortunately, the TX Constitution prohibits wage garnishment, so you don't have to be concerned about that.
If you can find a company that actually does relieve you of all of your obligations by taking over the ownership of your time share, that might be the way to go even if it costs you something.
Trouble is, you'll first have to carefully and thoroughly read and understand your time share contract and see if assigning ownership to somebody else (likely without the written consent of the time share company) actually does relieve you of your contractual obligations.
It wouldn't do to pay the assignee X dollars, assign the deed or contract, only to have the time share company sue you anyway if the assignee fails to pay the fees.