Russ,
Here are some proven loads that work great in the .444 Marlin:
BTB .432"-290g LFNGC/53.0g RL-7/WLRP/Rem Brass/2364 fps
BTB .432"-280g WFNGC/54.0g RL-7/WLRP/Rem Brass/2432 fps
BTB .432"-330g LFNGC/56.0g H335/WLRP/Rem Brass
Although there isn't a 300 grain bullet in the bunch, these all print under an inch if I do my part and are superb performers on game. Make sure to use a .432" diameter bullet for best results... regardless whether it is a Micro-Groove or Ballard barrel.
Hope this helps! God Bless,
Marshall