It looks like you were right. I can only get enough leverage to work the squeezer if I used only the tip, or the middle joint, of the bottom fingers. If I grabbed it like I found I'm doing with other handguns, I couldn't squeeze it. Also, I'd be pushing the weapon the the left.
When held correctly, there is basically none of the palm of my right hand touching the grips. It's just the fingers pushing the grip straight back into my hand. The P7 made me grip it properly for it to work. I still have to work on placement of the trigger finger, but that's a common fault I have with all my handguns.
I also received my Wolff spring kit today, and a new set of grips. This was a police weapon, and obviously spent more time in a holster than on the firing line. The old grips had slight wear on the texturing and edges, while the new ones are pristine. I also noticed that the subtle thumb rest has been subtly restyled. But this will be a working gun, so purists will no doubt be offended.
Now to try out the spring kit, and find the best weight (16 to 20 pounds) to use to replace the now-standard 21 pound recoil spring, which I think is overkill (overspring?) for 115 and 124gr bullets. I have fired 147gr rounds through the P7, and it was bearable, although a heavier Wolff spring would probably be advised.