Ok, I think I've found the fix.
I've not had a chance to test this yet but I noticed after cleaning my wife's vehicle that she has mats stuck to the back of her third row and they've been in place for years without fail. To my surprise, she has NO velcro stuck to the back of the third row carpet. She simply has the hook side of the velcro stuck to her mats and then the mats stuck to the back of the third row carpet. I only have two extra velcro circles left over from a previous attempt at making mine stick but simply sticking the hook side to the back of the third row seems to stick securely in place. I'm ordering more velcro dots today to try it.