I think it would work better to cut from "We must move quickly" to Palpatine's office directly. There's already too many takeoff/landing sequenes in the PT that just aren't necessary, and this is one of them.

The problem here is that if Anakin does go with them, why does it take so damn long for him to get up there? That was my only real problem with your edit (well, that and the fact that Palpatine A) still flips around like a monkey and B) uses a lightsaber at all; but I think B is, sadly, unavoidable in any ROTS edit).