Thank you, Scott. I had the same experience with my SP3: hovering my palm over the screen prevents the problem from appearing. When you did this test, did you have your surface plugged in or on battery? I suspect that touching the case brought your body's voltage to the same level as the surface, so that's likely part of the issue.
Back in 2009, I had a Wacom Bamboo USB tablet that experienced very similar problems depending where I was. When I was at college, it was fine, but back home 200 miles away (and 2 miles from strong AM radio towers) I was experiencing severe noise in my handwriting. Touching my computer case or any other piece of grounded metal made the problem disappear entirely. Wacom support wasn't able to resolve my problem.
I ended up selling my SP3 last week. I got to try out a Surface 3 (the new, non-pro model) at the Microsoft store over the weekend. I compared the handwriting on a S3 to a SP3 in the same store. Compared to my own SP3, the S3 there was much less noisy. I was deliberately drawing slow diagonal lines, small letters, and small circles, and it kept up well. If my SP3 had performed as this device I tested did, I probably wouldn't have ever noticed a problem in the first place. My hope is that MS has incorporated the pen voltage modification in these devices (the one alluded to in the Reddit AMA).
I'm hopeful that the Surface 3 does actually resolve the pen issue and they incorporate the fix into the SP3.