There is a technical difference which matters to me - in Av I can set one dial to change aperture and one to change ISO. P allows exposure compensation on the dial, but not ISO. Anyway, using P mode with aperture and shutter on the dials seems odd to me as they essentially control the same thing. If I used P I'd go for exposure compensation and program shift on the dials to get more control.

I don't get what you're saying, or I don't understand how SR works, which is very possible.
Surely the sensor can't be stable before the shutter is pressed as I presume it needs to be correcting in the opposite direction of the camera body movement for the time the shutter is open. So it's only when the shutter is pressed that it *starts* doing it's stuff. I don't see why the shutter speed should affect it's ability to make a mistake in that respect, or as you suggest, why SR shouldn't work just as well on shorter speeds. After all, the camera body isn't being vibrated more rapidly, it's just doing the same SR for a shorter period.