Paborn, for starters, your Verizon phone does not use a SIM card so that is out. Or, as suggested, go with T-Mobile in the USA and just buy a SIM card when in Thailand.
Better ust buy an inexpensive phone in Tukcom or wherever for your use in Thailand. People at the sales booth will help you set it up..
You can prepay and recharge as necessary. Can use AIS, True, etc as the providers. AIS is a good choice. EZ-PZ
Only problem is, if you want to maintain the same telephone number for the next visit, you must be sure to top up the expiration date . This is easy enough to do. If not then you would have to buy a new SIM card for the next visit.