Re: 300 or 338 ultra mag for LR elk gun
At the range, bullet weights and speeds you gave, here is the breakdown.
The 300 Ultra with a 180 Gr Barnes X Bullet with a BC of .552 will give your Dad 1988 FPS and 1580 FP of energy at 800 yards.
The 338 Ultra with a 225gr Speer Bullet with a BC of .484 will have 1696 FPS and 1438 FP of energy at 800 yards.
Between these two bullets the 300 Ultra has the advantage.
Now lets add the 338 250 Gr Sierra Game King here to your velocity and the BC is now .597 and at 800 yards the velocity will be 1907 FPS and the energy will be 2019 FP. The advantage now goes to the 338 Ultra.
I would go with the 338 Ultra and 250 Gr Sierra Game Kings and at a speed of around 3000 FPS. for an elk gun to 800 yards.
Just my opinion