Landing Visa a failsafe to avoid overstaying?

My visa/ARC expires on July 31, but I need to stay here until August 10 to do something ‘important’. I have one free day, July 31, on which I can fly out of and back into Taiwan. Can I just bop to Okinawa (or wherever) and get a landing visa upon return to Taiwan? I am just wondering if someone at Immigration will deny a landing visa because I am still technically on my work visa for a few more hours. Maybe the official I talk to will tell me, “Sorry, Mr. Taichung Guy. No landing visa for you. Ha, ha, ha. Just have a seat here for a few hours, then we’ll put you on a plane back to the States, hopefully a plane departing at 12:01 a.m. so you are not here more than one minute past your visa expiration date.”

I have noticed that many people posting here seem to have overstayed their visas for a short time: 1 day to 2 weeks. For all of us shameful overstayers, is a landing visa a failsafe (or at least a generally good way) to avoid overstaying? Everything I know about the laws and regulations tells me it should be; but, if it were, I would have expected to see the idea posted in the forum.