So I've just gone and tested it. Unfortunately, both LS + BFB will end up sharing the same cooldown with a 2.40 GCD =/

But... It looks like both BFB + LS could be double weaved with minimal GCD clipping... I think it clips for around 0.05s with my 84ms (WTFast + leatrix latency fix)

Could you try record yourself Thendiel and double check?