The solution, which was suggested by @paulvdh and procrastinated by me, was to start isolating layers and then selecting tracks with a smaller and smaller area, dragnet style, until I isolated a totally normal looking area of my L1 that appeared to have 10-15 tracks but reported to have almost 13,000 tracks.
I reduced my selection filter to just tracks, dragged to select the area around the problem zone, hit delete, and all of my speed problems went away.
Redrawing the tracks my circuit actually needs thankfully did not recreate the expunged 13,000 sements.
I honestly have no idea what kind of scenario would create a massive number of invisible tracks that did not count towards the track length counts. It seems very likely that KiCAD would benefit from some kind of track audit tool, or at least a troubleshooting note.
Anyhow, I want to reiterate my profound thanks to everyone who jumped in to help this newbie try and troubleshoot. I was on the verge of rebuilding my entire project from scratch and I’m so glad I remembered to try Paul’s suggestion before I did.