I tend to agree too..
Check the coax connections for continuity with a volt/ohm meter. Also make sure something isn't shorted between the center conductor and the braid.
Check the solder connections on both ends of the coax and make sure they're all solid and that they don't look like they were cold. Are they crimp on connections??? If so, get rid of them and solder your own on.
Check the whip on it's own and make sure there isn't a short in the whip between center and outer conductors.
Check to see how well the whip is grounded to the airframe.. Is their paint or some other insulating device that isn't letting the antenna ground properly?
Mentioned before: If you're transmitting indoors or in a metal building, it will affect your vswr and also the amount of energy that can effectively be radiated
away from the airplane.
Something you might consider is using a ferrite choke where the wires enter the amp meter. A ferrite choke will act as an RF trap/filter before it enters the amp meter. Some ferrite chokes are available at radio shack, but you might want a larger one.
Here's a photo:
You'll want to wrap the wire through the ferrite core several times, kinda like this.
After that, I'd probably try powering the VHF radio with a 12v power supply (or battery - just as long as it's independent of the aircraft's power system) and see if the problem still exist. If it does exist, you know you're battling an RF issue. If it goes away you know you're battling a power system issue or an inaccurate amp meter.