I bought a 77/44 a couple years ago used at a gunshow and took it to the range. I was getting 2-4" at 100 meters using 240 Hornady XTP with H110 and was very frustrated and understood why the previous owner dumped it at the gunshow. However, I started playing with it and noticed in the Hornady loading manual there is a listing for higher pressure loads for the Thompson Contender so I tried their top load because I felt the strength of the 77/44 was at least equal to the T/C. I was astounded when I got sub 1" groups at 100m. Then I ran the pressure series from below revolver max loads to the TC max load. I repeatedly started with accuracy at 2-4" and transitioned to sub 1" once I passed a certain charge weight threshhold. The change is repeatable and was very interesting.
I later found that the 44 mag is unique in that the spec for barrel diameter has 2 SAAMI defined diameters. Revolvers are .429" and rifles are .431. I believe this is because the first 44 mag rifle was Ruger's semi auto and I think Ruger used this to control pressure for the semi auto action.
44 mag bullets are spec'd for revolvers and not rifles. I think what is happening is that the undersized revolver bullets rattle down the rifle barrel giving crappy accuracy then are upsetting once they are hit with a certain pressure level and expand a bit. Once upset to rifle barrel diameter they give great accuracy from this rifle.
I haven't tried any other bullets because the Hornady 240 XPT suits my needs, but it would be interesting to try a hard cast bullet sized to .431 or .432 and see what the accuracy results.