I believe the history of the stops at (e.g) FCO, ZRH and FRA dated back way before the 70s. BOAC would have been the designated carrier for the British colonies and as such would presumably have had traffic rights between these countries and European destinations. Once the colonies achieved independence those rights would gradually have been extinguished in favour of the new national carriers. The availability of longer range aircraft and changing customer perceptions would have reduced the attractiveness of these stops too.
There were some new BOAC/BA routes in the 70s that might have been the result of negotiations over HKG rights: Seychelles via Orly, and Tehran via Dusseldorf come to mind. Then in the mid-eighties Munich was part of the through running MAN-MUC-DXB-BKK-HKG.
As for BEA/BOAC rivalry, both companies at one time competed directly on LHR-TLV with night-stopping aircraft leaving TLV within 30 minutes of each other. The whole history of the BEA/BOAC merger looks like a classic case of modern industrial tribalism - it must have taken ten years to get the two companies properly together. But enough said on that topic
