What steps should I take to ensure re-entry into Thailand after my work permit ends?

Hello everyone, it was suggested that I post on this group for some advice. I currently work as a TEFL teacher on a work permit. I will be finishing my contract here in Thailand in early October of this year.

In my passport, the provincial immigration department stamp shows I am permitted to stay until December 14, 2019 (picture in this post for reference).

I plan on taking a 2.5-week holiday in neighboring countries after my work is done, then I will re-enter Thailand to collect my belongings and move back home in early November. In the past I've gotten the "re-entry permits" at the airport before leaving, and I plan on doing it again before I leave for holiday.

Should I be worried about being allowed entry back into Thailand when I fly back from holiday? I'm kind of nervous with immigration since I technically wouldn't be employed anymore at that point. And I don't know how efficient my employer will be with departing paperwork, etc.

I was told that I'd have to turn in my work permit to my employer, then they'll provide me with a letter stating that I am done working for them. I would then take that letter with me when departing for holiday, then I'd be able to leave the country. Then when I come back to Thailand after holiday, I would just come back on a non-visa tourist stamp for 30 days in my passport. To be safe I was told to show a departing plane ticket and proof of funds when coming back into Thailand.

Can anyone confirm this is the path I should take? I hold a US passport if that helps in answering my questions. Sorry for the long post, thanks for reading!