So hopefully getting towards answering my own question....
In the case above, before adding mass, we have excess performance in terms of reaching screen height OEI, right? So would we have set V1 at the minimum speed that we can be assured to reach screen height/V2 after engine failure, rather than the maximum speed we can be assured of stopping within ASDA?
If the former is the case, I can see how an increase in mass would require an increase in V1. So there will be some speed range beyond V1 where in theory the aircraft will come to a stop within the (factored) ASDA, but we ignore this, because as long as we hit screen height on speed, we're happy? I suppose this fits in with a 'go-minded' philosophy..
Am I on the right lines?