Willie Walsh admitted to 4,923 who had their ST removed. On the reasonable assumption that almost all of these would have voted for a strike, plus another 900 or so who wanted to "send a message to Keith", then you've got the total number who voted to strike.
If Unite badly wants ST back in full, then why should BA just hand it back. Instead, I can see BA offering full ST back if Unite behaves properly and works with BA to grow the company. This would include no more court cases and no more strikes.
If Unite does not agree and goes on strike, then they will lose. BA will ride out any strikes and, after the 12-week protection period is over, Unite will not have the mandate for any more IA. I actually think that Unite is under more pressure to get a resolution than BA.