I don't quite follow. So do I perform this procedure BEFORE the pedal reaches the top of it's travel, where it normally would sit?
The 4x2 under the pedal is recommended and almost essential. Engine off. MC reservoir lid open. Reservoir full. (I just crack/leave front corner open. Put rags around as fluid will highly likely spill out.)
Hold pedal gently/ firmly at point of resistance. (Pump pedal if necessary to create higher point of resistance and then hold)
Open bleed screw and let fluid out for a second or two (Stop before the pedal hits the floor)
Close bleed screw
Release pedal and wait 10 secs
Repeat
It's all about keeping up the pressure and not allowing any air or fluid back in on the upstroke of the pedal/MC. I almost always imagine a bubble going back uphill while I wait 10 secs to push the pedal again.
If your handbrake has stopped working something isn't right. At very least the rear brakes need adjusting up. That will help you bleed more easily/effectively
Re air. A few seconds of clear fluid doesn't necessarily mean all the air is out. It all depends how much got in. Did the front of the MC reservoir run dry? FYI I've put over three gallons through my identical system recently. It's a PIA.
It's possible air is not your problem as an issue with the rear brakes could also cause you to have a bad pedal and handbrake. You should check the rear before you do anything else.
You could perhaps post in the forum here to see if anyone close to you has a tech2 to read any ABS codes you might have. Maybe a local brake shop would have something to read it. Otherwise it's a dealership. I just bought a Tech2 clone on ebay for $275
I one man bleed and that is not as effective as the two man process. But I need 40 pushes of the pedal to get about a pint of fluid from the rear passenger, then about 20 for RD. 20-25 for the front. If you're not aware you start bleeding at rear passenger, then rear driver, front passenger, front driver.
Hope that helps. Can't think of much more.