If you are on a long term visa you can just use your visa stamp. If you read the guidance notes it tell you that a visa stamp is fine (even though there isn't an address on it) I used my visa stamp 6 months ago.
apparently some Thai people have said that Robinsons in Petchaburi have a temporary office for passport applications but you will need to check first. Your girlfriend can go to Blueport Immigration in the basement as there is a Thai part to make a new Thai ID card and they should be able to confirm the nearest office.
you could enter on a 30 day exemption then go to Cambodia and Vietnam then return to Thailand on another 30 day exemption that can be extended in country for another 30 days if you need it.
it's an hour video that includes things about wearing safety belts and using an indicator when turning and then three simple questions to answer, anyone who can drive doesn't have to worry.
When I went I took the marriage certificate, new and old passports with the transfer stamp of my visa from immigration and also my husband. I had three different accounts from.different banks at the time and there were no issues to change my name and new passport number.
I transfered mine in a different province. My TM30 was done and showed I was living in a new area and it wasn't a problem but I suspect that it depends on the office which isn't unusual here.