Isn't there a problem here in that J cabins and Y cabins (not to mention W cabins) probably behave independently of each other in terms of demand.
In other words lower J demand does not necessarily mean that there is greater Y demand. Are there many who down trade from J to Y (not to W) on LH routes?
It is also necessary to understand the nature of the routes - I presume these are BA's Caribbean routes, as that is the majority of LH business ex-LGW. These are heavily leisure orientated.
On leisure routes passengers will normally book in advance and expect a discounted fare or purchase a holiday package of flight plus hotel or car. Few are going to purchase full J or Y fares and few are likely to be loyal to BA for the sake of it, particularly if a competitor such as VS is cheaper.
If you take out J seats, you are unlikely to get full fare Y sales. So at best you will be replacing unsold J seats with discounted Y seats, but you may also loose the potential to sell a discounted J seat.
Assuming discounted J = £900 and you gain 3x Y seats, you need to generate 3 extra Y sales at £300 or more to make up from loss of a J sale. If you are sure you can do this, then fine; but it would seem to me harder to shift seats at the bottom of the market where competition is more fierce, and the consumer more price sensitive and less brand loyal.
Then again, BBA must know its figures.