Congrats on the rifle, you got any pics of it? The Armstech's were the earliest Whites I think. I have a .504 White Armstech Whitetail and it is a sweet little rifle.
I would suggest that you get yourself some heavy lead conicals in the 450 to 500 grain range sized to match your bore and shoot the fool out of that rifle.
See what kind of accuracy you get with 70 grains of powder.
You might want to consider bedding the action if that hasn't been done already.
Art