So I got myself a Dremel and did as recommended - worked perfectly well. At first I had some doubts I could perform this operation myself, but it really was easy. Now all the grommets do snap right into place, sometimes with the guidance from an awl, and I didn't even have to heat them because there was no need stretching any part when going from hole to hole.
However, I am not sure if my final result is actually acceptable, as the grommets don't come out fully in the throat area. My question therefore is: Does stringing the racket take care of this by pulling the grommets tighter to the racket, or should I take them out and install them again?
Here are some pictures of "the situation" right now:
I started installing the grommets at the top and then went down each shoulder.
Any help would be greatly appreciated! I really would like to have them strung as soon as possible.
Oh, and for gear enthusiasts: Right now the weight of both rackets is 313 g, in addition to the CAP grommets, they both feature a Gamma leather grip and a Völkl V-Tac overgrip. In comparison to my MG Prestige MPs, the weight difference is 20 g (unstrung Prestige has Head Leather Tour and Gripsy Classic overgrip).