The .45-70 would have ammo more readily available than the other two.
I have no experience with the .375, but until you get into the real heavies. the .444 and .45-70 are two peas in a pod.
A .444 with a 1/20 twist barrel can move into the heavy-bullet territory quite well, and would remove a lot of the advantage a .45-70 would have.
As far as Whitetail, it would be a wash, with the advantage going to the .444 if using factory loads unless one goes with a light-bullet boutique loading in .45-70.
