I got a set of the TBHZ (passive) to try out, hoping I'd get close to the tone I was getting in those 2001 TB+, but without the noise. Nope. They sound almost identical to the TB+ in my 2013.
When I pick up my BC Rich at the luthier from getting a new nut I'll ask if maybe shielding would help the noise from the 2001s. My guess is no.