Most FM radios will be give good signals well to the point of being too dangerous to drive the car, as in you can hardly see what you are doing.
AM radios tend to be a different story as they are more susceptible to RF noise, but you still should be able to go more than 25 feet. I would expect an AM radio to give at least 100 ft of glitch-free range easily. The size of a nice track.
Some say that coiling your wires actually causes more glitching, not less, but the models I have had that I coiled servo wires on never had any issues.
You might even try placing your receiver on its side so that the crystals are on top, This is effective in Touring Cars with graphite chassis that create all kinds of noise.
I guess that you might have some damaged crystals as well, they can cause a whole range of problems from mild glitching to complete radio failure.