As others have said, if you want or need to fly in J you'll have to pay for it. Booking WT or WT+ and hoping for an upgrade will most likely end in disappointment, and in your case, serious discomfort.

Depending on where you're going you could try to break up the journey, tedious yes, but it'll give you a chance to stretch and lie down at the connections, even spend a night if you want to. 15 hours implies Tokyo, maybe HK?

In which case you could do something like LHR-DOH (6hrs on BA/Qatar), DOH-DEL (3.5hrs on Qatar), DEL-HKG (5hrs on Cathay), HKG-HND (4hrs on Cathay/JAL). Still means up to 6 hours at a time, and it does make the total travel time much longer, you might want to spend a night or 2 en route, but that'll still be cheaper than a business class ticket.