A 3 inch diameter mag mount setting flat on the automobile and having a paint/plastic thickness of 20 mils has a capacitance of 300 pF. The reactance is 38 ohms at 14 MHz and that is not a good ground connection.
So yes, a short ground wire is the thing to use. A 1 foot ground wire has an inductive reactance of 20 ohms and again that is not a good ground connection. The ground wire should be less than 3 inches.
The best thing to do would be to drill a hole for a sheet metal screw within about an inch of the mag mount, then run that ground wire directly to that screw. Don't forget to scratch off some paint, though, so the ground lug makes a good connection. That should make the mag mount work about as good as it can.
OH! WAIT! The whole idea was to not have to drill any holes! Maybe an on-glass mount? OH WELL! I didn't want a radio in the car anyway!