When V1 and VR are the same, runway lenght is not limiting ("infinite") for the stop case
Nit picking, I guess, but it might be better to say that the runway length may not be limiting. V1=VR certainly doesn't preclude the takeoff's being ASD limited.
why is a T/O never rejected after rotate but before lift-off?
Procedural protocol. In addition, operational technique may become critical from the viewpoint of repeatability for distances.
And remember that Vr is not a fixed speed either, it can be moved to enable a better climb performance after take off
Not really the case. VR generally is predicated on V2 and provides a suitable delta V such that, for the AFM rotation technique, VR will produce V2 - OEI - as the aircraft passes screen height. V2 may well be increased in some situations to take advantage of the improved climb gradient capability associated with an overspeed V2 takeoff.
When you calculate V1 you are using an unreliable fudge to find the point on a balanced field runway from which you may stop or accelerate to Vr before the end.
Not at all unreliable. Considerable effort goes into the flight test program and, for the conditions inherent in V1's establishment, the distance figures are sensibly repeatable. V1 does not necessarily presume BFL and can, for those aircraft whose AFM permits, apply for an unbalanced field length scenario.
I trust, for BFL, that you mean achieve OEI/AEO screen before the end rather than VR ? The latter might be quite disconcerting in many situations.