I mount GoPros on lots of different cars that are used for trackdays. My “go to” method is a a simple adhesive pad and shoe on the windscreen slightly to the passenger side and below the rear view mirror. To ensure good adhesion I clean the contact area either with brake cleaner or an alcohol wipe - something to remove any traces of dirt or grease. And I then fairly loosely attach a tie wrap between the fixing bracket and rear view mirror stem. I’ve never had a mount come unstuck.
I personally think the view you get from this camera position is very good, although many people prefer mounting further back in the car so you can see the driver inputs etc. That not a problem for cars with cages, but somewhat more challenging where this isn’t the case. Fixing the the OE roll hoop,(as you’ve already mentioned) should work, but obviously you’d need something like a cage or handle bar camera mount. The only tip with positioning would be to hang it below rather than above the top of the hoop. My only slight concern with the OE hoop is whether it would vibrate at all. Also, of course, you would be able to take a passenger with you.
Here are a couple of vids showing the two different views.