I'm with Brent, I still think there is a DC ground issue.
However, given the information regarding your mounting location (sorry I didn't ask about this earlier) you also have the issue of a poor image plane. Basically, the truck surface needs to act as a ground radial for your antenna, and your location doesn't allow this very well. You could correct somewhat by using a taller antenna to get above the vehicle more, but it won't make a large difference.
Instead, you could use a 1/2 wave antenna which acts like a dipole and uses the coax as the other half or ground radial. I've seen some surprising improvements by moving to a 1/2 wave for locations with a poor image plane (both with 11m CB and 2m/70cm Ham).
The best result though would probably come from a change to a no-ground-plane antenna system (which is specifically designed to use the coax as a ground plane). I know Firestick offers these and I'm guessing others do also. I've never had to go this far though, so I can't offer any personal experience.
As for why one radio worked and another didn't - that's confusing. An intermittent DC ground problem would certainly explain it, but you would need a lot more test data to confirm this (couple hundred attempts with each radio).
However, I've also seen marked differences between radios when connected to the same poor image plane antenna, even though there is little noticeable difference in the two radios when connected to a quality antenna with a perfect DC ground and excellent image plane. So in short (no pun intended) the poor image plane magnifies any weakness in the radio's transmit ability.
An antenna analyzer would help here, but I wouldn't recommend the expense if this is your only purpose. However, I would recommend you find a local Ham radio club and get to know them, as someone there will likely have an antenna analyzer and be happy to help you out.
As a final note, the image plane issue is supported by the fact that your mag mount worked well. Though mag mounts generally have a poor dc ground, they often have a great image plane b/c they are generally placed in the center of the roof or very close thereto (and in any case much better placement than a low point on the front bumper).
Keep at it, you're getting close (I can feel it)!