Sunday;
When you set a specification of "300 yards" you have effectively eliminated the .444. You may be able to reach 250 effectively, but 300 yards is realistically beyond the reach of the short, stubby bullets of the .444, even the 300 grainers. Even with the 356, you have reached the extent of its reach also. You are working with flat nosed bullets that shed their energy fairly quickly.
If you reduce the range specification to 250 yards, either with do such easily. Then it is a question of personal preference. Both with do the job, with that limitation. I would prefer the .444, because it looks more traditional in a lever-action rifle. Then I would look at the Buffalo Bore bullets of 270 gr and 300 gr.
Hope this helps.
dclark