Due to a new glitch found called Equip Swap, you're able to skip hookshot which was one of the main timelosses for English. Then combined with other English-only tricks like Mikau cutscene skip and a faster Turtle Cutscene Skip, English is about 20s faster optimally. It's a small difference however, only worth it for the high level players.

Though top players like thesausage and Ennopp don't even go for the English TCS. I can see why. With the current route, it is night when you're at Zora Cape. I think the SoDT TCS skip only works during the day, like English Mikau CS skip, but don't quote me on that.

So if you have to play Song of Double Time twice, I can see why the JP TCS skip is faster, since it's basically that skip with English loading zones.

That is correct. SoDT Cutscene skips require a Day to Night transition because of the fadeout that happens. Without that, the cutscenes don't get skipped and it's the same result as if you tried a SoDT cutscene skip on JP.