Very curious why windshield or dashboard suction mounts aren’t an option. They work great.
Also not sure why you are intent on using a GoPro as a dash cam. It is both overkill (cost wise) and very poorly optimized for the task. You can get a proper dash cam with proper dash cam features for as low as around $30, and $100 will buy you a pretty high-end one, whereas the cheapest GoPro is what, $200? And with the GoPro you’re dealing with either limited battery life or a custom mount to keep it plugged in, limited recording time, no looping, and of course as you’ve noted here, difficulty mounting.
If you are intent on using the GoPro as a half-featured dash cam, I think the mounting solution for you is going to be a beanbag/gravity mount. There are plenty of options on the market, I’d just get the cheapest one with decent reviews on Amazon. Combine this with a simple suction mount and you’re good to go, with no trouble pushing it right up against the windshield instead of way back at the edge of the dash wasting half your field of view on the dashboard as you would with a hypothetical vent mount.