It is a good idea to have your re-entry permit before you go to the airport.
Not long ago I had to leave Thailand suddenly on business and did not have a re-entry permit on a new retirement visa. I was delayed in traffic and the desk was open but the attendant was not present. After a few anxious minutes someone showed up, took care of it and I did not miss my flight.
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