That the hum goes away when you touch the bridge usually indicates that earth is OK. To reduce the hum, your best bet is shielding. This is tricky in a semi hollow as you really want to contain all the electronics in a Faraday cage. That said, any extra shielding is helpful. So putting some copper tape in the cavities is not a bad idea. Ideally the shielding should be grounded as well.

To your other point regarding the pots, it's possible you have them wired back to front. Just double check that you have used the correct outside tangs. The center tang is the sweeper and looking at the bottom of the pot with the tangs facing up the left hand one is the output. You can actually swap those two around, but not the outer two (as you may have- ALSO I'm still learning here so if someone know better please correct me)

Finally, as long as you will be looking at the pots, just make sure all the connections are good and you don't have any stray bits of wire touching stuff they shouldn't.