Follow up... we got home too late last night for me to even try to test out some new scenarios, so I just finished up and here's my findings:
I realized that my Scarlett does not rely on USB for power and had its own power supply, so I was able to take the unit to another part of the house, along with the GR 350 and plug it into an outlet that no other power was being drawn from that circuit breaker (trying to minimize any interference on the line).
The results were nearly identical as my previous findings, maybe a slight improvement, but I kinda expected that, so I wasn't disappointed.
In further experimentation, I found that if I used an XLR to 1/4 plug (DI -> Scarlet), there was no noise at all, and the bass signal came in clear, though lower in overall volume than directly from the DI using only XLR. I'm not sure what technically may have occurred to remove the noise from the signal, but using this method worked for me (prior to this situation, I had used the DI out on another amp into my Darkglass Element to add cab emulation into my DAW - yes, I am aware that I can add a plugin in Reaper for the IR...). I also found that there was no noise when going from DI to XLR into my interface only on certain knob positions on the DI volume with the GR 350 (ie 9:30 & 11:30 are two that stick out).
Yes, there is definitely an issue with the DI, but I am at the point where I'm going to keep the amp (for the smaller gigs) and not worry about the issue (when I do go to sell this at some point, I will be disclosing the issue and my findings and adjusting the price accordingly). I honestly don't have the time to look for a budget friendly lower wattage amp, so I'll live with it.
Once again, thank you to all who added to the conversation, none of which I've taken bad - its been very informative.