I see... Indeed, my only goal when adapting Shivers Sort was to maintain some invariant that would make the analysis easy, while mimicking the arguments developed by Buss & Knop for their analysis of (plain) Shivers Sort. It is, however, sure that the n(H+4) upper bound I get should be refined when H is small, which more or less amounts to tackling the 3-run case you mention.

I am reasonably convinced that the current version of Adaptive Shivers Sort could be adapted to take this problem into account, while keeping its overall simple stricture and complexity analysis.

If this first step turns out to be feasible, I will also look at the latest version of runstack.py to investigate other possible improvements on Adaptive Shivers Sort.