@Steve ******
Damn. It used my local time zone when I checked so it was actually showing me appointments for Tuesday when I clicked on Monday 🙁
I still think going may be your only option, but I'm not sure how busy it is at different times of day. It's actually a very very bad day to need to go after a 4 day weekend.
Technically, though not recommended, you could make a Tuesday appointment and just pay the 500 baht overstay fine and then extend, but I wouldn't want an overstay stamp in my passport.