Jerry PA: You are shooting one of my mostest favorite calibers. I have always thought the factory loads were somewhat understated for this caliber, especially with regard to bullet weight offerings. I was very happy to see the Hornaday Light Magnums come out for this caliber and find that the 265 gr bullet they offer is leaving the barrel at the same velcoties we used to reload them to. Good, it's about time.
As for your question regarding the Remington 240 gn bullet used in the Remington factory loads and those for the 44 magnum that you have laying around, a recent article in the 4/04 Shooting Times by Joe Coogan who took his Marlin 444 on an Argentine Red Stag hunt provides that Remingtons original offering in 444 used the Remington 240 gr bullet they used in the 44 magnum. Remington now offers the cartridge with a 265 gn load that vastly improves the performance of that cartridge.
My personal preferences are for the 300 gr or heavier bullets. However, for what you will be hunting, the 240s are very good. They are very good on larger game too. One of our other posters took a large cow Elk with an 80 yd broadside shot that dropped her in her tracks. They recovered the bullet under the hide on the far side. That's pretty good performance for a pistol bullet at rifle speeds, and that load should drop any whitetail if you place your shots properly.
I've taken a fair amount of game with a 444, including black bear, moose and squirrel, and whitetail. Most of my loads have been with the 265 gn bullet but a fair number have been with the 240s. I didn't have any problems with either bullet. With 500 slugs hanging around you can get in a lot of practice and get to know your rifle well.
If I may suggest - if yours is the 444S with the Micro-groove barrel, you may wish to firelap the bore to obtain better accuracy. Beartooth Bullets as well as Veral Smith sell firelapping kits and the result is a more accurate rifle. HTH. Mikey.