In line with the last few posts, yes the latest Boeing performance thinking does allow optimisation of assumed temp/de-rate/improved climb all at the same time.
It's unlikely you'd get improved climb on a short runway, though unless there's a howling headwind.
Rummaging through the book, I doubt you'd get de-rate or assumed temp reduction at BRS. *
V1 split would be less than 5kt so the answer to the "would it have flown with a V1 cut?".
Probably.
At our place we have expressed surprise at the amount of runway we seem to be using these days, but if the book says it's fine, eh...?
(Not getting drawn in to the rotation technique in this case).
* That's assuming we are close to perf limiting mass.