I'm very familiar with ball check valves, which is what the Speed Bleeders are basically. But since the general consensus is that they are useless, I'm going to ditch them or sell them cheap to someone who wants them.
I think I'm going to get the vacuum pump system, that I included in my first post, sometime later this year. There's a cheaper version, but it seem most reviews describe it as worthless junk that often breaks the first time out of the box.
I still want to replace the brake fluid for the rear brake line and there is not as much of a gravity flow with it as with the front. The vacuum pump arrangement might come in handy with this.
Brakes are working fine now, nonetheless. And I now know my front brakes have clean, fresh fluid in the lines...

And my ride was great this afternoon !!

Steve