Dave,
I have had a 1-4x VariX-II shotgun scope for almost 20 years. It was on my slug gun for 12 years, until rifles were legalized in my area of NY. It withstood around 300 rounds of 12 gauge sabot slugs during that time, and helped me shoot 15 or so deer.
The eye relief is great, never had an issue even when I tried Patition Gold slugs-much more kick than the .338 Fedral, I'm sure. The only complaint is that the heavy reticle does not allow precise bench shooting (not an issue on the shotgun, but I used it on a 7mm-08 one year when I was lacking for a scope-my groups were about 1/2" larger than usual.) Leupold will swap out the reticle for a standard duplex for $60-haven't decided whether or not to do that. I think the 2-7 will be a good fit for the .338.
PS-Thanks for the advice about Encore barrels-still have not decided between the Federal or a quarterbore.
Will