You have until 23:59 on the last day to leave Thailand without overstaying, not 24 hours. Actually, it's your responsibility to cancel your extension based on teaching. If you are still on the first 90 days from non-B, you cannot cancel that stamp and you can stay until that stamp's up.
IF your passport country is eligible for visa-exempt entry, you can enter again for 60 days on visa-exempt even on the day you leave Thailand.
IF your passport country is not eligible for visa-exempt entry, you have to apply for a tourist visa in another country (which takes 5 days to a few weeks) before entering Thailand again.
[edited] That is totally made-up story. As long as you have a TM30 receipt your extension will be 30 days for tourism purposes, regardless of the length of stay at that address. Just make sure "checkout date" field is not past date or it's open.
Or just submit now with the address where you currently are staying. There is no rule like that you can submit TM30 only once with the same address.
Currently, there are no written rules on the maximum number of entries on the visa-exempt scheme, regardless of whether entering by land, sea, or air.
But it's possible only until the officer at passport control gets doubts about you being a genuine tourist. If you keep doing border-bounce, eventually you will be pulled aside at the entry point and asked about what and how you are doing in Thailand.
The only immigration office where you can do a 90-day report on your DTV entry in Bangkok is the ChaengWattana office. Go to the Government Complex Building B.