Both are simple, but if you don't have another need to be at immigration, the airport is fine. No need to make a special trip. I've never waited more than a few minutes at the Suvarnabhumi re-entry permit desk. But if you're at immigration for other reasons it's also simple to get it done at the same time.
Re-entry permits come in single and multiple re-entry. Single permits cannot be used more than once, multiple re-entry permits let you use it as often as you like. Multiple re-entry permits are only available at the immigration office that issued the extension of stay. The airport booths are open
Sjef van Ballekom going in with your pink ID Card, yellow house book, and Bangkok Bank app doesn't really work in your favor to show you are a genuine tourist
. I've made it a point to maintain a personal relationship with a banker at my bank's HQ and that has helped in a few situations. When you go to pick it up take that person a something small and grab their name card. It may pay off in the future.
Don't bother with BBL at Central World, go to the Silom head office and go to the second floor to the international transfers desk. These are the only people at the bank that can help you.