Mudslinger,
I've had a 444 Marlin since way back in the mid 1970's. Wouldn't sell it for any reason. I love it. It's a fine cartridge for close range thumping. My 444 accounted for my very first deer, and also a wild boar. My son took a large boar with it also. I took the deer with a 240 gr. Remington factory load, and the two hogs were taken with handloaded 265 gr. Hornadys.
What surprised me the most is it's accuracy. When I bought it, I didn't expect that it would deliver such good accuracy. I load IMR 3031 and 265 gr. Hornady Flat Points that will group practically touching at 50 yards, and shot three shots at 100 one time that resulted in a nice clover-leaf pattern, all three touching. Man, that's accurate for a big bore rifle.
I also loaned this gun to friend who showed a buddy how accurate it is. They busted bottles at over 100 yards consistently with it. He tried to buy it from me and I wouldn't sell.
Bear over bait or up a tree would be no problem, I think. You might also look at other bullet choices, heavier. As for Elk, I personally would not use it unless my shots would be very close. That being said, if that's the only caliber I had to hunt Elk with, I would feel confident with it. I have no experience on either bear or elk, but I'm just stating my opinion. Others may have solid experience and info that might shed more light on that.
You won't go wrong with this cartridge for deer and wild hogs. Just realize that it's slow moving, a real thumper at close range, and accurate. Use it within it's limits and you will be very happy.
My son, Nelson, age 14, and a record book
Boar, shot while bayed by dogs. One shot
put him down.