Your first point of worry is the airlines you travel on as some may require proof of exit. In the Thai immigration side, it is a coin toss. If your travel profile is good and you do not look like you are trying to live in Thailand without a proper permit, you will probably have no issues. But if you are repeatedly going in and out on visa free tourist stamps, you may meet some resistance

If they stamped on your passport that they refused you entry, if I am not mistaken, you automatically will be banned for a period of time. So no matter if you use an agent or try flying in, you will still be refused. If you did not get stamped, you will still need to get an agent to check and hopefully try to get a proper visa

In some borders, citizens may be able to travel across with just temporary visas by using just their local id. But if I am not mistaken, it is just for the area near the border, eg the nearest town. But to go on a flight and actually need to pass through immigration, I am pretty sure a passport is needed.

It is kind of a hassle to actually need to get out of a country and go to it's embassy in another country tp get a stamp or a piece of paper and so on. If we were to be in country, immigration should at least give us a letter whereby we just need to leave the country, come back and hand that letter at immigration and they just stamp our passports and it is done. It is just hassle.

I personally do not see any issues with your current mode. Because you may be staying in Thailand for a certain period but you fly our regularly and within your visa limit.

The only sticky thing I may foresee if it gets too long, like maybe over 180 days or maybe even a year, then it starts to be pretty obvious that you are trying to live there without a valid visa and that could become troublesome.

Just my thought though. Maybe you could do a DTV which allows you up to 5 years and 160 days per entry. Then maybe it will be "safer" for you.

For me, I would pay the money and extend the visa because you could get an overstay stamp and other hassles later if you overstay. Also, if the airline postpones the flight to an even later date, you would be getting into further issues.