The flights need to be in a continuous forward direction between T1 - T2 - T3.
(b) Travel must be in a continuous forward direction between TC1 - TC2 - TC3.
Further, the availability of surface segments between continents is extremely limited:
(g) Intermediate surface sectors are permitted at the passenger’s expense. Transoceanic surface sectors between TC1-TC2 and TC1-TC3 are not permitted. EXCEPTION: For travel originating in the South West Pacific, one transoceanic surface sector between TC1-TC2 or TC1-TC3 is permitted. The first crossing between TC areas must be flown, not surfaced.
Imo BA is correct and you will need to return to Europe to restart your AONE4.