The screw thing is weird. Does the screw head just sit straight on the handlebar, scratching it up? Is the front bit rigid, providing a platform, or is it just basically all silicone?
I agree with the idea of getting a garmin quarter lock mount. It's a handy way to attach things, lots of cheap generic options, including those using silicone rubber bands, and it makes the challenge as simple as drilling a hole, assuming the mount doesn't have the right size for that screw. You can get this on Aliexpress for a couple dollars with either free shipping if you buy a few more dollars worth of stuff or a couple dollars shipping.
If it makes you feel any better, the bridge is missing an entire suspension line and is going to fall on him right after this moment.