Coming at this from the running side, on the analysis half rather than the gear tools.
Shoes do move those numbers, but pace moves them more. Ground contact time and vertical oscillation both track speed, and step length is close to a restatement of speed and cadence. So one session average against another mixes shoe, pace, terrain and how tired you were by the end. Tagging the shoe removes one source of noise out of four, and not the biggest one.
What works better is to stop comparing sessions and compare a fixed slice instead. Same route, same pace band, early in the run before fatigue starts stretching contact time. Hold pace and freshness still and a shoe swap shows up clearly, and so does a form change.
That got easier last week. ryandev shipped the running dynamics as real streams on 3 August, with per-interval averages: stance_time, stance_time_percent, vertical_oscillation, vertical_ratio, step_length, leg_spring_stiffness. Thread here: Working on advanced running metrics (GCT, Vertical Oscillation, Vertical Ratio, Step Length) — help us cover more devices before we ship it - #19 by ryandev
Per-interval averages mean you can pull the same warm-up lap at a fixed pace out of every run and line those up, which answers most of your question without gear on the activity. The gear tools would still solve the mileage half.