interesting that badly done shielding can cause noise, when I strip it down again I'll check continuity between each cavity shielding, that may be where the break has come.
Shielding is, to some degree, like building a big net to capture electrostatic interference. That interference is then sent to the ground side of the circuit. Single coil pickups are prone to capturing electromagnetic interference, which cannot be easily removed (enter the realm of dummy coils and other technology). You could use twisted-pair wiring to cut down on EMI, as well as shielding.
It might be worth checking continuity between all the strips of slug tape you used. Copper shielding tape is manufactured with a conductive adhesive, whereas this isn't necessary to keep slugs off your lettuce, so don't assume anything! I would solder a wee joint between each strip of copper tape if you don't get 100% emphatic electrical continuity across all sections of your shielding.
On the flip side, some people find that an extensive shielding job actually kills highs due to the capacitance of the shield interacting with the wiring in the guitar. I also believe there is a bit of a 'ghost in the machine' element, and simply taking time out to unscrew everything off your instrument then screwing it all back together will have a profound psychological effect outwith any sort of electronic improvements! I hold 'Guitarnutz' accountable for creating a lot of panic about the need for shielding and star-grounding guitars.
A final thought, Gibson shielded the back of their control cavity covers, but didn't ground this shielding or apply any additional shielding to the cavity itself? Why?!?