I flew out of the country with both passports. An employee of Thai immigration pulled me to the side and transferred my visa stamp onto my new passport.
-Painless process, it may have taken 15-20 minutes and I didn't need paperwork.
Upon re-entry, I had scheduled an appointment with Elite Visa staff to transfer my Elite Visa 5 year sticker. She walked me through immigration and they stamped a new 1-year visa onto the new passport.
-Painless process, 15-20 minutes again. Perhaps 20-25 minutes from my gate to the taxi area.
-They required my Elite Visa card (in my case a photocopy, front and back) OR the original letter of acceptance that you receive upon gaining membership.
For now, I am uncertain if I needed to redo my TM-30. I can see both arguments, yes and no, as I have gone through major official channels.
I chose to not redo it and I'll update you on whether or not it is the correct thing to do or not after I do my 90 day notification, which I have to go to immigration for on the first attempt anyway.
Note: I attempted to do a 90 day notification on my new passport prior to leaving the country and was rejected with a notice that said I had to go to immigration on a new passport for the first 90 day.
I left the country prior to being in the country for 90 days, so there is no "overstay" on the 90 day reporting.
We will see. Thanks to everyone for the advice. I appreciate it and will update you with what I learn.