Absolutely a run up to Mae Sai for a border bounce is the best option but a small overstay (2 days) is an alternative - I did a 6 day overstay myself at the beginning of 2016 but only because Promenada refused a 7 days extension Dec 30 as my ED (and extension of stay) expired Dec 31. \
Seven days only, then pay then 1,000 baht overstay on the way out. Payment at CNX is easy, you pay it on the left just as you pass international security and there are zero hassles. You could of course just overstay 9 days but it would be cheaper to get the 7 day extension then pay the 2 day overstay.
Tip - if you dont want to share your passport number you need to cover up all three instances. Also make sure you've got at least 6 months validity left. Im pretty sure M series passports were phased out in 2009.
Chulia Mansion is brilliant and right near Jim's Place so you can use him to do it for you. If you absolutely want to do it yourself, book a Grab car, it's not a costly ride.
Yes, it's a 500 baht per day fine for an overstay. You'll pay it on the Thai side and get a small stamp in your passport for good measure. There shouldn't be any dramas when you get to the crossing. Technically if you're caught on the way to the border on an overstay you could be detained, but it's highly unlikely one day late - if asked, tell them you're heading to the border.