There is something not quite right, you have obviously been flagged as suspected living here and working illegally or the IO wouldn't have suggested a non b. You say in the last year you have entered 14 times for
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weeks at a time so you have spent well over more than half a year inside Thailand. You could look at getting a DTV, if you meet one of the criteria then you would be fine for the next 5 years.
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.