First of all, IMO, I wouldn't re-wrap them unless the wrap has serious issues.
That said, sometimes a re-wrap is necessary. So, here's my experience with 60s Ludwig 3-ply:
As you said, "part of the wrap is goes into the shell joint" which was just the process they used, at least up until they started using the granitone interior in the 70s. They may have made the switch sometime during the clear maple interior days, but the painted white interiors all have the wrap into the joint (at least all of what I've seen). This IS a pain in the rear!
I've used a utility knife and carefully cut through the wrap right at the seam so the old wrap (that's in the joint) no longer shows. Then carefully remove the old wrap, usually with heat (BUT -- don't let it get too hot, as it can easily catch on fire!!).
Now, the sad part: It really don't matter whether you use the tape or glue method, you're going to have somewhat of a "flat-spot" at that seam. Now, it's not uncommon for Ludwigs of this era to already have a bit of a flat-spot at the seam anyway, but when rewrapping it does seem to be a little more pronounced. That's just the nature of the beast, I guess.
Good luck...
Bill