Speed Bleeder should make it easy. I have on of those too. When pumping, make sure the speed bleeder is opened about half of a turn. It takes time (maybe 5-10 minutes with a Speed Bleeder?), and you won't feel any pressure in the lever until the line is full and the bleeder is closed. You need to pump slowly. I've heard people talk about "priming" the MC to get things started, which I think means disconnecting the MC, filling the bore (and putting your thumb over the bore hole to keep the fluid in) and then reassembling. I didn't have to do this, but maybe worth a try if you continue having issues.
Regarding the rebuild, the things that I think people can sometimes get wrong is installing the MC piston seal backwards (so the seal is facing wrong direction), and not cleaning the two reservoir holes well enough. The return hole is very small and often gets clogged shut. If that's clogged then I would imagine it'll be hard to fill the lines (and your brake won't work properly), especially if you have the reservoir cap on. Try with cap off, to relieve any vacuum pressure you may have, but make sure to pump slowly or you'll get fluid jetting out.
Hope this helps,
Aaron