I personally don't like any of the methods on those pages, unless I missed something, and prefer to do it this way (the way that the Corvette service manual advices):
Open the brake fluid reservoir cup and remove as much of the fluid as possible while still keeping the bottom inlet area under fluid. Top off the container with new clean fluid.
Hook up a drain tube to the farthest (rear passenger) bleeder and open it. The force of gravity will cause the fluid to run out. Keep an eye on the reservoir, keep it topped up. Once clear new fluid runs cleanly from the bleeder, close it.
Repeat for all 3 additional brake fittings, moving close to the reservoir each time.
This method is considered the least harsh on gaskets and seals. Older Vettes apparently have a problem with some seal if you use a power bleeder or pump the brakes during the job. This can take a few hours to do, but it's not very intense and as long as you are keeping an eye on the reservoir, it's not bad at all. I think I did my Cherokee in about 2-2.5 hours, so the smart should be faster.