You can still use it until the Valid Until date, then go to plan B after it expires. Remember, if you leave Thailand and return just before the Valid Until date, you will get another 90 days.
I use 2 uk PP's one for Thai non O (Thai spouse) and one for Vietnam (TRC). In and out of Thailand on 1 PP and in and out of VN on other PP. I also get my non O visa from the hcmc consulate on the PP that doesn't have the VN entry stamps and TRC.
It could be an option for you if you can't get it done at land borders.
... get a certificate of residency from Immigration and yes you need it to get a DL. Not sure what all you need but certainly a copy of the lease agreement but best to check online the full requirements and of course you will need to have done your TM30 prior to visiting imm or you will get fined.