Well, I went ahead and bought that 3M emblem adhesive as well as took a good look at the orignal wing badge. I Cooper one sits way far out when just placed over the Cooper-wreath. I used a heat gun on it to loosen and took a pick to the original emblem. Figure I was going to cover it anyway, right?
Turns out there Cooper-wreath is made up of two parts. The first is a thick, clear plastic cover. That came off easy after the heat with a sharp, thin screwdriver.
The actually printed Cooper-wreath was tricky. It is (rather nicely) printed on a metal backing. It is also very tight to the edge of the opening. I had to add more heat and really work this one out. Once removed, I noticed that there were two holes in the back of the wings that might have made it easier to push out. Either way, I got it out with any damage to the wings.
With both layers removed, the Cooper emblem fits nicely and much more flush. Very happy to have these on finally. Also, these were brand new genuine Rover wing emblems that I started with. Might not be as easy on an old emblem that has had the sun and age make things difficult.