Rix,
"Beefy" strap probably would do it, as long as it's bare metal to metal contact at the block/terminal/frame. Would it be "constant"? Yes the ground would be constant, but in the case of not having one or having painted surfaces, the ground would be marginal. The ability of the armature to turn when heat expansion occurs would not. In other words, when cool, there would be less energy needed to overcome any resistence, as compared to hot. If the ground is marginal, it wouldn't appear to be a problem at cool, but when energy requirement increases it could be insufficient.

Based on your latest experience I wonder if your solenoid or the terminal connections are the problem.