Why don't BA just do what UA does and you have a few lines roped off for different classes/zones.
I know space is limited but you could easily change the fast track line to be F/J, the Eco line to be Gold/Silver and then you let everyone else board after that.
If there is no queue management then nothing will ever change as it's just too difficult on a consistent basis to hold back the masses (and the gate agents just get bored trying, sooner or later)