Speed bleeders from the "Help" rack at your local A/Z or DiscAdv. are one of the best gizmos ever invented. The key to any bleeding is to "take your time" when pumping out the air. On my 54 with a completely new upgraded system I used 12 slow pumps to clear each of the four wheels. 12 pumps, refill the m/c, do the next wheel, etc. However, if your using a step-bore m/c the procedure is completely different. A s/b m/c can be identified by a larger diameter bore close to the mount and a slightly smaller bore towards the front. If a step-bore is not properly bleed it will be difficult if not impossible to completely bleed the wheel cylinders.
I would suggest you get 4 bleeders and start out just like you had replaced the entire system. 12 pumps on each wheel should remove all the old contaminated fluid and give you the braking power and reliability you need.