Here's a comparison of a normal chain grab strat VS a chain skip +big boost to lever (before the fake sister / box factory section).

NOTE 1: reaching the lever much sooner doesn't seem to skip the rotation of the level, thus making the skip much less significant (only ~1sec time save).

NOTE 2: pls ignore the mishap at the end ... got distracted having to stop the timer at the ledge grab after the box push :(