I would start by using shielded cable between all of the components and by shielding the pickup cavities. Maybe try that first. If you're not hearing much noise, then doing more is probably overkill.
If that's not enough, you might be able to do something like what the old Danelectro's did. Make a box out of cardboard that fits over the components that you can attach to the pickguard or control plate. Cover the box with shielding tape. Make sure the shielding tape is grounded to the jack. Drink a beer. (You should turn off your soldering iron before the last step.)
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