What if you enter twice by air then can you enter once by land? I feel like they might confuse the policy and say no, you've already had 2 exemptions, you can't enter by land.
I'd personally do the exemption and extend while here. You just show up and pick a day to go to the immigration office, pay 1900 thb and you're done. I feel like the applying for the visa option would be more hassle. Having to send bank statements, accommodation info etc etc.. Whatever suits you better though.
I changed passports when crossing by land from Cambodia to Vietnam. As one of them gives me visa free entry and the other doesn't. Seemed to go pretty smooth although I did have to explain to them why I was doing it.
I understand your question. I've done that trip to Aranyaprathet/Poipet before and it would be the same for someone with a Danish passport as it was for me. Apply online for the E-visa before you go, getting it at the border will be more hassle.