Orbit -
Thanks for the good description. I wasn't familiar with the Baggs pickup which is why I keep making mistakes about its specifics (it's passive, etc.). Each followup prompts me to do a little more research...
First off, you don't need to try to debug the output jack connection. When I looked up a picture of the Ultrabass pickup, I realize what that round thing in your picture was. The coax cable from the pickup element is going into the Ultrabass jack assembly and this was assembled at the factory.
The white wire you see is a coax cable. There's a thin conductor running down the center of the wire which carries the signal from your instrument. It's surrounded by insulation and that's wrapped with a foil or braided metal shield, then there's another insulating cover around the shield which is the external appearance of the wire. To avoid hum, that center conductor must be surrounded by a grounded shield over it's entire length to the output jack and continued over your guitar cable to the amp. The shield blocks electromagnetic fields in the air - if there's any gap, the EM field will leak into the signal and cause hum.
So, this whole grounding discussion had to so with whether the full length of the cable was shielded, particularly where it connects to the output jack. It's easy to make a mistake there when you're wiring up a regular output jack like a Strat or Les Paul. In your case, Baggs built the output jack area inside a metal housing, so you don't have to do anything special.
The bad news is that it's starting to look like there's a damaged conductor or shield in the pickup assembly or ourput jack and that may be hard to fix.
The best test for this kind of problem is to substitute a known-good pickup for the questionable one and see if the problem goes away, which is what you suggested at the end of your post. If they have a unit out, you can just hold it against the bridge and see if there are buzz or output level problem. That's cheaper and faster than any test you can do on the Baggs.
I've never used an external buffer, but what you're looking for is an external preamp that has at least 1 megohm input impedance and hopefully 10 megohm. On the low end, you can get a Fishman BII (around $50). There's probably no limit to how much you could spend on a buffer, but devices like the D-TAR Solstice (this has two channels and EQ) would be around $325. Baggs has a product called the MixPro which would also work (this one looks like it's $160).
If you're changing pickups, then you might look for a system that includes a pickup plus external buffer amp.
David Fung