I cannot speak for Concorde but it is often the case that a range of V1s are available with reference to take off performance. It is, of course, necessary to select one V1 to use on a particular take off.
There are many (airmanship) factors which might impinge on whether one would use a minimum or maximum V1. For example, if the end of the runway is a vertical drop down to the beach (aka Madeira) one might be inclined to use a min V1 since the last thing you want to do is go off the end but being 34 ft at the end of TORA/TODA would not worry you too much. Conversely, you might you a maximum V1 if, in the engine failure case, a significant emergency turn is involved after take off. On the other hand you might pick a speed between min and max V1 as a compromise.
All this assumes that a range of V1s is available. In the case of limiting perfomance this may not be so.
PifPaf, in some companies this concept is taught and practised - it's all a case of "gilding the lily" if you want to. The concept of V1 is, some might say, somewhat outdated but it is a simple system that works quite well.