Not sure if things have changed or I misunderstood, but you now go thru immigration stamp out and then go apply for your reentry visa at Suvarnabhumi immigration, I had to confirm as I only had a single entry visa , and on a side note the long term parking at zone A is a bargain at 140baht per day for those leaving briefly and free shuttle bus to terminal
TLDR : Answer Summary
When departing Thailand, obtaining a re-entry visa can require different steps based on recent changes in immigration procedures. According to recent experiences, travelers must first go through immigration for their exit stamp, then apply for their re-entry permit at Suvarnabhumi Airport. However, some users suggest that it may also be possible to secure the re-entry permit before exiting if you confirm with Thai Immigration officers upon your arrival at the airport. Additionally, the long-term parking at Zone A offers a cost-effective option at 140 baht per day.