Lots of reading here that should answer your questions, though this is mainly on reloads with cast bullets. I've shot up to their 405gr. casts in my 444P "Outfitter", but I believe that one has the cut rifling Ballard bbl. Basically, you have to go to a .431 diameter cast bullet to get the best accuracy and least fouling, especially in the older micro-groove ones.
The Hornady 265 gr. FP is a great bullet for jacketed ones and was designed for the 444, not for the 44 Magnum like many other bullets.
beartoothbullets.com/tech_notes/archive_tech_notes.htm/17
beartoothbullets.com/tech_notes/archive_tech_notes.htm/19
beartoothbullets.com/tech_notes/archive_tech_notes.htm/28