It sounds like you like the weight of the bass, if it is not TOO heavy for you, have at it to make it the way you like … I have had many of these, I do not keep them if they are over about 8.75 lbs, that eliminated most for me … I do not consider these
light basses in general ...
The 'very high action' triggers a red flag for me on these, as I have came across a handful that had neck issues, they bowed badly … I fixed a couple in a jig with pressure and time, but I passed on a couple that were real bad … FWIW, the issue seemed to run in this model during the '06-'08 run, so you should be ok … the ones I usually kept were from '01 and '02, the first two years of these for some reason really seemed sweet … I only bring it up to make sure you are aware of it before you go spending $$ on it … you sound like you have been around the block, so you can tell if the action is correctable and not a neck issue … I actually started using Reggie Hamilton bass necks on these bodies, exact same neck, only the Reggie had a 9.5" radius board vs. the 7.25" on the 60's … vintage fret wire and all ..
If it bothers you, absolutely shield it … I never shielded any of these, but I almost always matched volume settings, and if I came into a room that was an issue with lighting, etc, I would just use something else …
I am a moderate fan of these pups, have one USA bass here currently with them in, they are a very inexpensive set by most standards .. it surprises a lot of people that they are used in so many models over the years … MIA early Hwy 1's, American Specials, Classic Series 60's and 70's Jazz, and even in the Road Worns (Fender adds a 4 to the neck part # and a 5 to the bridge # which designates the relic applied) ... I believe this is also the pup that they are using in the MIM Geddy since they moved production in July of 2012 …
I am not a fan of active J's … passive with either LaBella or Sadowsky flats
BTW, if you haven't had the pickguard off, you may be in for a pleasant surprise … no channel routing