The only ground required by the solenoid is for the pull-in coil inside it, and that is accomplished through the safety switch.
All the shielding in the world wont prevent it only a detuning of the circuit.
A year or so ago I walked into a class at the U where I was taking continuing education classes.
That led me to searching YouTube.
Will the cheaper unit work? If that is the case, you have to replace the rectifier.
I hope it's clear what I'm looking for.
Red goes to + on battery Black is ground.
This point could be placed anywhere on the secondary circuit without affecting the working of diodes and all remaining components.