How can I obtain a re-entry permit at Suvarnabhumi Airport, and is the booth easy to find?

yes, the booth is at Section 2 . . visible behind the glass from the departure level. You either must go upstairs, pass through the security scans before you go back downstairs and can access the re-entry booth BEFORE you pass through the Immigration desks. Or if you have a VIP Card, you walk through the security at the departure & check-in level, but then right after the scan must make yourself heard that you need a re-ntry permit, as the next step would be the immigration. Tell the personnell after the scan

Re-entry service is open at Suvarnabhumi airport. If you do not have all the documents, they charge you a 200 Thb service fee.

Not sure about them being open at that time. If I were in your situation I would go to the nearest immigration office. Multiple entry applications take almost no time at all. Even at Chiang Wattana