On the Beta I always remove the caliper pucks to remove the spooge that gathers in behind them. You can't ever get a guaranteed good bleed as the fluid will not flush through the circuit in behind the pucks. split the calipers, remove the pucks, fill the pockets with new fluid, install the clean pucks, and reassemble. Better brakes in most cases.

I was going to suggest you might have a piston or two not doing their fair share because they are stiff and seizing in the caliper due to ingress of grot.