BA used to offer an "upgrade on board" capability, whereby you pay the purser after you board with a WT boarding pass (and a WT seat assigned). But this may be considerably more expensive than the OWE WT+ upgrade fee which is a relative bargain as well as being unlikely to be available on this route as the WT+ seats often go before the flight. There is zero chance of WT+ seats for upgrade being released before the week of your flight; if you had a bit more status (2 levels more) you could ask for yield management to release a seat (some travel agents also have enough clout with BA to do this, if they have a lot of high-yield business).