I have found that my 44s in general, and particularly my SBHH like the heavier bullets(300+gr) much better than the lighter ones. Accuracy with the 240s was acceptable, but with the 300s it shoots teeny tiny little groups. As a note, and to add credence to your results, I once tried some Blazer 240gr JHPs...those bullets shot what was closer to a pattern, not a group, at 20 yards (at least 7"). Tried a different ammo and tore the X ring out of the target.
The 300gr XTP is a very good bullet. If you want to shoot jacketed, then this would be on a short list of bullets to use.
All of my Ruger 44s shoot cast bullets pretty well. If you decide to go that route, there will likely be some fiddling around with loads and bullet diameter to get the most accuracy and minimal leading. Myself and a number of the other guys on this forum can give you some very good starting points if lead is what you want to shoot.
This image has been posted here before but here is what can be wrung out of that revolver and an UltraDot red dot.
2.35" 4 shot group off of sandbags at 100 yards
P.S. The pic was taken on my workbench, so no, that is not a bullet hole in the wood.