And the Hewlands were not available till early 1960's, well after BRM started building cars.
BRM built their first gearbox for the V16s using inspiration from pre-war Mercedes-Benz. They built gearboxes for 2.5 and 1.5 litre rear engined cars -- quite well, it appears. At the time they did not have much of a choice. However none of these earlier designs was appropriate for the V12 pumping out 400+ bhp so BRM designed a new five speed box. (I'm unclear how this was related to the H16 gearbox.)
Gearbox design and manufacture are specialist activities. If we look at the history of 1950s and 1960s rear engined cars, we can see how difficult those activities are. Cooper continually fettled the ESRA/Jack Knight designs, Colotti gearboxes were initially unreliable, and even a big firm like ZF struggled in the early Lotus 49/Cosworth period. Other Lotus experiments are best forgotten...
I can understand why a constructor would make a gearbox out of necessity or because they could make a significant improvement (six speeds). However BRM had already established that the Hewland options were good enough. Not Invented Here was part of BRM's mentality but I struggle to understand why they thought they could do better. If you are taking a design risk, surely there has to be a significant benefit?