Coils don't "wear out" so swapping the knocker coil to the kickback didn't really do anything. When you moved it did you leave the lugs on the coil pointed up, so they contact the underside of the apron? Ditto for the outhole kicker if you messed with that at all.

The logical direction is to reverse everything you did - despite your best efforts with pictures, etc. you've got something wired incorrectly. For instance, if the diode on the coil happened to be mounted the other way and you were keying off a logical path of "this wire was on the left lug" you would have reversed the hookup if the diode was the other way round.

The weak coils are most likely from dirty coil sleeves, worn mechanisms, old lubricant on mechs (most of them DO NOT need anything, and the ones that do, use VERY LITTLE. Do NOT use WD40). You could also have a low voltage condition in your location, or the transformer could be wired wrong, the bridges could be bad/weak, the connectors on the power supply, a compromised wire in the power chain.