I've been down the exact same road as you have.

I own an Eezibleed and find that it does a fine job for moving fluid through the lines slowly and with very little force. So, if any air gets trapped in the caliper at any point, the air won't be forced forward and out the bleeder.

So, what to do?

Firstly, the old method that Tom has ascribed will work, but it certainly is not necessary. I can bleed the brakes in 1/3 the time as compared to that procedure:

Get yourself a tall bottle (like a horseradish bottle) and fill it 1/3 full of brake fluid. Get a hose that fits the end of the bleeder screw. Shove hose on bleeder screw and open bleeder one full turn. Place other end of hose in bottle, below the level of the fluid, and stand bottle on driveway so it won't tip over.

Go back to driver's seat and press pedal slowly down and slowly release. Repeat 10 times.

Return to wheel. Carefully close bleeder screw by rotating hose. Keep opposite end in bottle. When screw is closed, remove hose and tighten bleeder screw.

Check reservoir to be sure fluid level remains above "min".

Repeat for second wheel (assuming you are only doing the front wheels).

This procedure is a one man procedure and is guaranteed to work as good as, or better than, the two man procedure. As an added plus, you are not jamming the bleeder screw against the stop 10 times.