Good questions. To reply to your last point first, hopefully I am not being arsey on here and I am with you on the pro/anti thing, I have stated my stance, or lack of, previously.
You may be correct re the bargaining unit, I have not read the full law, only precis, but suspect that it is direct RYR contract only. Brookfield are a contracting company, it says so on their website
Brookfield Aviation - Providing Human Resource Solutions Worldwide
and as such they may withdraw from RYR at any time. At our place we have agency staff of equal responsibility status but they have no place within our industrial relations. That is why I advised RSS to go see a lawyer and meant it. If BRK guys are in dispute they are in dispute with BRK not RYR.
As far as I am aware there is no provision in UK law to vote against anything, only for. Unless it is a referendum. Hence -
the test for this is at least 10% of the proposed bargaining unit are members of the union and a majority of the proposed bargaining unit would be likely to favour recognition. A petition may count as evidence.
That is why BALPA are running a petition on their website and requiring details be posted in confidence so that CAC can prove its voracity which is not true of the workplace 'ballots' being discussed on here.
You mention 5 of 10 bases having voted against. Leaving aside its validity (see above), if that translates into a majority of the bargaining unit, which takes us back to point 1 re composition of such, and they are not BRK then all is well and good for the anti camp and RSS may retain his dummy in his pram. If the results do not accurately reflect the intentions of 50% + 1 then the dummy gets airborn and it would trigger a ballot. Recognition, if won, would be accross the company and not on a base by base basis, it doesn't work like that in UK. There would be no hypocracy involved as 50% + 1 of the bargaining unit would have voted for it of their own free will.
Hope this helps.