Wow, that's a pretty tall order. Let me make sure I understand what you are asking. You want to hang a $500 dollar, 3.5 pound radio from a couple of suctions cups, like a $100 dollar, 8 ounce radar detector? You can experiment with some things, but I'm not sure I'd take that chance, lol.
That double-sided 3M pressure adhesive tape might work in place of suction cups. It's surprisingly secure stuff, for sure. I'd still be very wary though. Best case failure is a broken radio. Worst case failure is a broken face.
Although pricey, the BC-RH96 remote control head would be a viable option. I'm not sure what it weighs, but it would be secure enough with suction cups or heavy duty velcro.