KL is a good option, as mentioned above. If you're flexible about times you can get a return for around thb2,000. For an extra 1,200 you can also get fast track in the way in - great for avoiding queues at Immigration if you're flying in at a busy time and want to avoid fighting with Mainland Chinese for 2 hours.
The re-entry permit counters at BKK and DMK are both 24 hr now. The office at BKK used to have patchy hours but since they moved the service past security screening it's always open .
Your certified marriage documents don't contain a police background check. Maybe you're getting this confused with the affirmation of freedom to marry?