Follow up: My wife called the Seiko Service Center in Bangkok. They advised that we could drop off the watch at the Seiko Center at The Mall here in Korat. They said it would take about a month!
We dropped the watch off this past weekend. Oddly, the service guy seemed quite concerned that my watch says "Movement Singapore" on both the face and the back. He said he'd never seen that before. All the watches of that model either say nothing or "Movement Japan".
He confirmed that the watch should have at least two days of reserve time after being fully wound. He also said it would take three or four weeks.