@Bill ********
just get the right to marry document notarized at the US embassy, and get married at your local Amphur. It is actually pretty easy to do, as your Catholic wedding here meant nothing. Official marriages are done by the Amphur, and registered at the same time. The Catholic marriage would be considered the same as a ceremony with all the monks, not an official marriage in Thailand.
I would slow down, get married at the local Amphur, then start the process at the US embassy of getting her green card. You can do it here. Then both of you would be off the tourist restrictions.