How can I extend my stay in Thailand after my tourist visa expires, and avoid immigration issues?

Urgent advice needed

So here's my situation, Pattaya based. Arrived into Thailand 5 months ago, 30 day visa on arrival. Extended it for a further 30 days, then did a few trips to Cambodia every month and most recently went to Laos and got a 60 day tourist visa which is now due to expire on the 5th of this month. I fully intend on staying in Thailand for at least another year, if not longer; having spoken with a School here that most people recommend for an education visa they tell me 14 days (30 recommended) is needed to fully process the application which clearly I don't have.

I could easily just fly out again and come back, but I'm very worried about the amount of stamps I have already. the last time I came back from Laos the immigration officer pressed me about why I stay so long time in Thailand without a long term visa, I'm afraid if I do it again I will have problems :/

Trying to recall conversations I've had with mutual friends here I seem to remember someone saying, if you come back via bus/minivan there's a way in which you can avoid being grilled by immigration officers, is there any truth in this? Is it a case of a little extra baht is paid when coming back over the border and no questions are asked? This will be the last time I need to make the trip in such a risky way so I need to ensure I'm able to get back , soon as I am I will start the education visa process. I fully intend on attending all classes, if I'm gonna be living here learning the language will be useful