What are the steps to obtain a marriage certificate in Surin, Thailand, for a foreigner with multiple divorce decrees?

All of the steps are listed here and can be done in a few days (including a trip to Bangkok)

Only needed my last divorce decree last year.

You are technically not married at this point. You will need a right to marry document from your embassy, and being divorced you will also need your divorce decree documents. These documents with your passport, and copies, copy of your wife's ID card, you take to the local amphur, along with two witnesses, and get married legally, then it is recorded. You leave with your marriage license, and registration document. You might need to make an appointment before hand, but, they will not make an appointment before you have the right to marry document from your embassy, translated into Thai, and stamped as being an accurate translation by the ministry of foreign affairs. An agent can't really help you.

The first thing I would do is go to the Surin amphur, to see if they will do it for you. It is usually only amphurs in tourist areas like Pattaya or Bang Rak (in Bangkok).

You will definitely need to go to the US embassy in Bangkok and then to get the documents translated then to the consular affairs department (you need appointments at all these places). You will need a translator and witnesses for the ceremony also.

I would recommend getting an agent to help (I didn't, but it would have been much simpler and probably cheaper than multiple visits to Bangkok, because it is not that expensive). Good luck.