Unless the camera is cheap junk, its shutter was designed by someone who knew their job, and if it could easily have gone faster, it probably would have.
On some mechanical leaf-shutters, the top speed does involve an extra spring, I think. Certainly it's tangibly harder to cock the shutter at that speed.
I suppose you could buy one really good leaf shutter, with no lens mounted in it, and mount it on the front of any lens, when you needed the extra speed (with the camera's own shutter open on 'B'; like the old Thornton-Pickard roller shutters (I don't think T-P shutters themselves went faster than about 1/100). Being run exposed to the open air like that might not be good for the shutter in the long term.
If you're struggling with too-bright light, the easy answer is an ND filter.