The BA web booking system can manage different classes on simple A=B-A transactions. It can't deal with it if you want an open jaw (which you do). Your choices are to make the booking both ways in the same class online and then hope that manage my booking will offer you an upgrade.
-OR-
use the phone.
Stupid? Maybe? Cost you more? Probably but it's worth pointing out you are booking something that you can't book online; that might change their mind.
If you insist on dealing with BA direct I think what I'd do is phone them, ask if you can make the booking you want and find out (a) what the fare is and is it available (b) then I'd ask about the simple economy fare and what the fare rules are for that - does it allow you to upgrade and are there any fees to do so and what the additional fare will be (c) if they will charge you for using the phone. Then I'd take a deep breath, book economy and then go straight into mmb to upgrade and if that failed go back to the phone.
However, the easier solution is probably to phone someone like Trailfinders who can not only book your flight but may well be able to provide you with some of the other elements you require.