Some tele lenses might have focus ring go a little past infinity. That is to allow for temperature changes to the body (amongst other reasons). And maybe for IR photography too (I don't know for sure).
300mm lens is another example. The ring will go a little past infinity.
But many lenses won't fire at 1/1000: these are the PQ lenses. Only PQS will do that. In PQ case the camera won't allow 1/1000, regardless of whether you use a flash or not.
I don't know of any firmware in the lens that can change that. I would guess you need a shutter change at the very least.
I have tested all my lenses with Hy-6 back: 40mm to 300mm. And none have any calibration for this back. The results were awesome of course, so no malfunction there. All are non-AF PQ or PQS lenses.