What is the fastest and safest way for my Polish friend to re-enter Thailand on a visa exemption?

You will need insurance to enter if you fly in. Your friend's from Poland, which has a 30 day visa exempt policy. %20on%20Arrival/VOA.pdf

I would try to see if he can get a visa to Myanmar. If he can, try flying into Myanmar, and then figure out some way to cross back by land. He may be able to also get a tourist visa from the Lao consulate, and then fly into Lao, and then cross back via Friendship Bridge.

He does need to cancel his extension of stay. If he has already stopped working, then he is already on overstay (not good!). If his contract ends on March 31st (or whenever), then he's fine.

I'm assuming of course he has not used both of his visa exempts by land this calendar year.

Health certificate and Insurance is already in place as far as I understand