Brief update:
I spoke to the BAEC and said that IB-coded VY-operated flights would count; however, I booked the itinerary with BA as of now (and the flight appears with a BA codeshare on my ticket) so that should count as an eligible flight (marketed by British Airways)

I am still hesitant on whether to 1) fly this with BA and get 3 eligible flights 2) fly it with AA/US and fly business for the same price