It would appear that the GP fender liner is not your plain 'ol standard MINI. Located behind the forward part of the rocker panel and lower trim, there's a flat tab on the rear-most part of the fender liner. It has a hole in it which is held in place by one of those two-piece fasteners and it doesn't appear accessible without removing the whole rocker panel. Anyone ever successfully done so without removing said rocker panel? If so, please share the method!

 

Bump!

 

O.K. I'll answer my own question. First of all, the wheel well liner is standard MINI. It's just that the rear lower tab is hidden up underneath the GP rocker panel. I accessed it by first drilling a 1/4 inch pilot hole directly beneath where the fastener is located, then used a 1-inch hole saw (which has a 1/4-inch pilot drill in the center). That gave me enough room to use a long Philips head screwdriver on the center piece and a long scribe to hold the outer piece from rotating. If the center piece won't retract, you may need to use a long drill to ream it out. Once removed, it's fairly easy to remove the wheel well liner. When re-installing, I'll insert and screw in a new fastener through the hole and into the tab, then use a 1-inch black plastic hole plug to seal off the hole.
Removing the rear wheel well liners requires a similar operation. You have to remove a Philips head screw that is hidden from view by the GP rocker panel. I gained access to it by using the same 1-inch hole saw at the rear corner of the underneath side of the rocker panel. After installation, I used the same 1-inch black plastic hole plugs.