I'm in the final throws of booking an xONE4 itinerary but have had my route rejected by the BA ticket desk. They say that I have exceeded the permitted number of stopovers in my continent of origin. The relevant bits of my route are as follows.

1. GIB-LGW
2. LHR-NRT
...more segments...
17. SFO-LHR
18. LHR-DXB
19. DXB-LHR
20. LGW-GIB

I am currently trying to book segments 1 & 2 as a transit without stopover. I.e. segment 2 commences within 24 hours of the arrival of segment 1. Segments 18 and 19 are currently open. Segment 20 has a specific date.

I see this as being valid in that I have one transit without stopover (1-2) and two stopovers (17-18 and 19-20).

Can anyone shed some light on who's right and who's wrong?