I'm happy to say I have an update on the noise front! I'll update my posts above to reflect my finding just so that it doesn't cause any undue concern among readers future forward.
I set everything up for my usual recording chain again today, tested that it was quiet with my StingRay, and then proceeded to plug in my Player Precision, and still - buzz city, though again, it could be mitigated by lifting the ground on my DI.
I went through component by component for my entire audio signal, and nothing helped. So then I started working on other things that were hooked up. Not my laptop power supply... not my mouse... and then I unplugged my secondary monitor!
I didn't get complete silence - I'm not so naive to expect the same low level of noise as I get my active 'Ray, but acceptable golden silence-ish nonetheless! It was my secondary monitor all along, and I couldn't be happier!

In fact, it was so happy, that I decided to just do a little down and dirty sound sample that I figured I'd share. Please disregard the sloppy playing, these were just to have some quick sound samples on hand for reference with the bass by itself, and then through my recording chain (basically just my VTDI). Both obviously use my Player Precision with the stock strings (that I still dislike

):
Player Precision and Fresh, Stock Strings Direct:
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Player Precision and Fresh, Stock Strings + VTDI (mind my fumbles, at at least one point I went searching for my nonexistent B-string)!:
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