Pressure filling the brake system from the lowest point is a great idea, as Adam notes it carries the "I want to float upwards" air - upwards. I don't know anyone with a pressure brake filling tool; these are required to service many ABS systems but are hardly a normal home shop tool. Excepting Jay Leno's "home" shop maybe...
I had a great deal of trouble trying to bleed and de-air my own front brake lines, not happy with the spongy feel at the lever after installing braided lines that were supposed to get me a firm lever feel.
The speed bleeder is pretty neat, but assists only in traditional top-down bleeding. It's purpose is to prevent air being pulled back into the caliper when pumping fluid down using the M/C - it has a one-way valve so you don't need to do contortions to loosen and tighten the bleed nipple every lever squeeze. You put grease on the speed bleeder threads to stop air being sucked past them.
I tried a large syringe for brake filling from the caliper, it worked OK but fluid naturally leaked past the bleeder threads and made a mess - you can't use a speed bleeder (one-way valve is the wrong way for this) so it has to be swapped in after finishing and that process leaks more fluid.
As noted, brake fluid will squirt out of the M/C relief hole up to the ceiling easily when pumping it into the caliper , squirting the farthest when the reservoir is empty with no pool of fluid to squirt through. It always manages to spray onto - and ruin - nicely painted surfaces. Hopefully forum readers have learned this the "easy way"!
My solution:
First I measured the caliper piston height at the point where it is just in over the cylinder seal, as I recall it is just shy of being level with the caliper face.
Then fill the system the usual way, from the M/C - but with the caliper piston fully pushed in and held with a C-clamp.
Then loosen the C-clamp and pump more fluid in until the piston is at the measured height for maximum volume of fluid in the caliper cylinder, and leave very little fluid in the M/C reservoir - put the reservoir cap back on to catch the squirting.
Then use the C-clamp to push the piston back in all the way, with quick twists on the clamp screw to hopefully shake bubbles loose.
I shake and tap the caliper (dismounted, obviously, to get the clamp on) with the brake line inlet upwards, dismount and orient the tee likewise and shake/tap it, hold the flex lines so that any upward arcing bends that would collect bubbles are eliminated, watching the reservoir level to syringe out excess fluid before it overflows.
After a few repeats, the result was excellent: the brake lever feel is very solid. Brake operation is better as well, the initial brake drag after applying the brake is almost gone. I think that air in the system defeats the slight caliper piston pull-back effect as the M/C piston retracts before it uncovers the relief hole.
You get the de-airing benefit of a $$$$ pressurized brake system filling rig for the price of a C-clamp and a syringe.