Wire might be rubbing on the inside of the thick PBT, which has less room inside than a thin ABS key. Cherry stabilizers don't have this issue, as they interface directly into the key and keep the wire more out of the way. You can see if the wire rubbing is causing the binding, figure out which side is causing it, and then correspondingly shave away a bit of the inside of the key so that the stabilizer has more clearance. I've seen this done before, not sure if it was on vintage or repro keys, but to solve the exact problem you have been describing with Cherry thickness and Costar stabs.