I asked as I was sitting next to a couple in immigration last week who had not done that and were on a 60 day tourist stamp. I suspect the lady you spoke to just couldn't be bothered as your stamp clearly say Non 'o'. Just try again at that branch if you are set on that one or try a different bank.
Gov.uk provide all the information. Your main objective should be that she has a strong reason to return (job, family and property) and provide evidence.
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.