Setup for hitting the gate wcs after gruz mother which, contrary to popular belief, is ~0.35 faster than the normal movement with no chains (1). After finishing cleanup, do 4 nail slashes and then quickly dash near the top of the gate. Continue holding right until you touch the ground (or the wall) then jump and dash to the bench (it's possible to chain the jump dash and still land on the top platform but it's very tight)
For an additional 0.2 timesave, you can chain the wcs and do a second dash midair with a nail slash (2). To input this, go neutral to uncling, then slash (direction doesn't matter but you HAVE to be neutral during the slash) and within 6 frames, press right and dash. Generally I land early enough to where I can fit in an extra dash and jump with coyote frames to the bench, but if you land further to the right you can probably go for a chain instead. The frame window for this is not super tight but it's a really awkward input that's very hard to greed, and if you mess up you'll be zooming to the left and lose one quantillion years so this might not be worth for runs but maybe it can be improved to save more time.
If you dash through the gate too early and don't make it over the ledge, you can back it up with the normal movement and still save about 0.2 (3). For TE and other categories without claw, the 4 nail slashes can also work as a good setup for pre-dashing through the gate (4).
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