what did you do with your fazer today ?

[unfazed]

Do you have access to a vacuum brake bleeder, it is as you have found out a pain trying to do it without one.
Gravity flow to let the fluid drain out works well in a non ABS setup but not as well on ABS setups.
Other option is use a large syringe to pull the fluid through and out of the system and to pull it through to refill it.

Do not  turn the ignition on while you are doing this. 

When finished and the brakes work again take the bike out and get the ABS to kick in a few time to allow it cycle the fluid through the ABS unit.
If after the ABS kicks in the brakes feel soft bleed the brakes again.
I changed the screws on the Master Cylinder Cap, see Picture