How can I switch passports while obtaining a Non-B visa when flying out of Thailand?

Hi everyone, I have a bit of a strange situation:

I must fly out of Thailand due to no more Covid extensions for me.

I plan on flying to Phnom Penh and coming back in with a 3 month non B (I don't have a work permit yet).

So; during this fly out and back in, I also want to switch up my passports since I have 2. However, my school is telling me they can only get a letter of approval for me on the passport with a current visa which I'm currently using in Thailand.

Is there any way around this? I was thinking:

1. Apply for an E-visa on my 2nd passport and have my school try apply for the letter with that.

2. Stay in Phnom Penh for an extra week and mail copies of the Cambodian visa in my 2nd passport once I've flown.

Any help would be much appreciated!! 🙏