You don't think if a player is incredibly sheltered zone wise by the coach that it would influence even a little what players he sends over when a rush is developing. Maybe I'm a pessimist.
A difference of 30% is quite low for the extreme cases (percent difference of like 55% between guys getting 40% and 70% usage) assuming I'm understanding your use of delta which likely should be normalized.
Even using those numbers 3% more offensive and 3% less defensive zone starts would have a pretty decent impact when your comparing corsi values that are represented using standard deviations of small relative differences in value. These differences in the corsi values being compared are likely much lower than a percent difference of 15%.
Personally I prefer to look at unadjusted stats and get all the context of zone usage, QoC etc my self rather than looking at these regression heavy models. Lots and lots of assumptions built in.
Assume 100 shifts:
Player 1 w/ 70% offensive zone starts:
70 shifts start on the fly
10 shifts start off neutral with zone faceoffs
14 shifts start off with offensive zone faceoffs
6 shifts start off with defensive zone faceoffs
Player 2 w/ 40% offensive zone starts:
70 shifts start on the fly
10 shifts start off neutral with zone faceoffs
8 shifts start off with offensive zone faceoffs
12 shifts start off with defensive zone faceoffs
That's about 6-7 games worth shifts, where player 1 gets all of 6 more offense zone starts.
That's not going to have a meaningful impact on possession statistics.