This would be relatively easy to modify. If the driver could be extracted from the cup, you could build up the cut-out depth for the drivers by about 1/8". There are more than a few ways to handle this. Some small layers of tape inside the cup and slightly over the recess for the driver. This would ensure the driver could not be presed too far into the cup. You could also use some adhesive to build up the bottom of the recess, so the driver does not go too far into the area. Or, glue in a few pieces of toothpics towards the bottom of the recess. Again, all those options would prevent the driver from sitting too deep into the cup.
It would be an excellent fix in your case as it seems like you've tried many pad variations with differnt levels of success ... and also some pads that didn't make the sound too pleasing.