LittlePope is right... the copper shielding kit from StewMac is about half the cost of a set of Fender brass plates with the foam... and for shielding, properly installed copper foil might be (edit: is...) better, but you're still going to need to put something between the wood and the pickup to raise the height.
For my 85' MIJ 62RI Jazz that I just gave a 50,000 mile checkup I shielded all the cavities with
copper foil shielding kit from StewMac, and dropped the brass plates back in beneath the pickups... I didn't go "full stewmac" and replace the pickup leads with the coaxial wire (included in the Jazz bass wiring kit, which I also bought for the replacement pots) Might be a belt and suspenders solution to some... I just wanted to keep the brass plates to keep things "original" The end result though? Perfect. Dead quiet.