I used to mount the GPS unit to the windscreen in a mobile phone cradle, with a cable tie around the GPS unit and cradle to hold that together, then another cable tie from the cradle to the roll cage in case the suction cup failed. Mobile phone went in my pocket
I used it more for post-race analysis than a laptimer during the event.
Since I put the new roll cage in, I attach the GPS unit to the front leg of the roll cage with race tape and the phone goes in the mobile phone cradle. Unless its Regularity, then the phone still goes in my pocket. No timing allowed in-car in regularity, I figure having it in my pocket meets this requirement, yet still allows me to record for later analysis.
I tried to used double sided tape at one point, just didn't work.
I don't need power for GPS or phone - just charge them up beforehand and there is enough battery life for a day on the track.
My QStarz was around $100 as well, pretty sure only 5hz, but that was at least 6 years ago.