My best guess is that cable isn't traveling freely. It should absolutely be plopping into place. No heroics or chainline DIY required :) The first thing I'd do is take the chain off and actuate the RD from high to low, even adjusting it so it will travel a little past the last cog, just for the test. It should do this effortlessly and without any friction. The RD itself is easy to test by taking off the cable and actuating it by hand high and low, it should move easily. If all that is good, then there's a hang up in the cable itself. With the cable end unattached, grab it with some grippy gloves and move the shifter up and down, it should move real easy. If you feel friction then there's something off with the cables.
I just realized I missed the rollamajig part, big oops ! I never used one, but frankly I'd start there, after I wrote all that ! Simply try the RD without out it. If it works fine, then there's obviously something about the rollamajig. Again, I never used one but I see it has a cable adjuster, I assume you tried that ? It could be it's simply not allowing the RD to travel as it's supposed to, as in too much tension and the cable isn't going far enough to go into the last cog.