I very much doubt that there will be any attempt to woo strikers back to work over the second strike. WW has stated very publicly that strikers will lose their ST permanently, why back away from that. I suspect it is more likely that those on strike now will not be allowed to come back to work until after this is all over.
BA will know after this first strike what is possible in terms of flights for the second period of disruption. They will be able to make plans for this coming period of disruption with a far greater certainty than they were for the current strike. This means that they will be able to provide the public with a cast iron programme for the second strike. Based on yesterday it is possible that this wil be a slightly bigger programme at Heathrow and a normal service at Gatwick. It is unlikely they will want to do more than that.