I just wanted to report back after having my Apple Watch replaced by Apple last week. Since replacement, I have run about 25 miles in different locations (open space, trees above, trails, roads) and the performance of the new watch has been spot-on. The tracks are completely reflective of my movement, there is no jerking or location points that have me across the street. The pacing is consistent and aligns with my perceived effort (and importantly, checking the distances against a few online sources like "How Far Did I Run?" etc, the distance checks out) and historical pace. This is all while connected to LTE and using LTE to stream music, podcasts, get text messages, etc.
Hopefully this may help someone in the future if they're still having this problem. This is obviously non-scientific as it is only one experience, but this does make me wonder if there is a hardware difference between my old and this new watch.