Highflyer. Moraly you are right people really should only either vote or sign the offer not both.
However, I don't think you need to worry about the figures not adding up because in all the previous votes so many crew have not even bothered to vote. The turnout has been so low and basically it seems that apart from people like you and me, and all the other passionate posters, mostly only NO voters vote, which is why they got such a large % vote in favour of a strike.
I know that alot of crew just stayed in to vote NO to a strike and really want to be able to accept the offer. I think you are morally right but no one in either BA or the union can be sure of the membership. The union office must be in total disaray they have barely enough staff to deal with the disaplinaries let alone their paperwork.
None of us want them to strike again and voting to accept the offer might help to stop this but signing will also help to show BA they have our backing.
So I think the only people that will suffer if someone was to vote and also sign would be the union. So don't worry too much.