The 300 yard varmint/PD is not a problem. In fact, with custom barrels and forends they are going past 600 and it is just a matter of time (good conditions) before they reach a 1k PD.
200 yard elk with a Contender

I don't know enough of the JDJ cartridges in 33,35, and 375 to know if they work effectively at 200 yards. You can surely take elk with the 375 JDJ you mentioned, but I would think the 338 JDJ (whichever is the right one in the contender) would be better in terms of trajectory and recoil levels.
Contenders are not my specialty so if I am describing something wrong, please correct.
I'm thinking Encore or bolt rig where your options are about endless.
A good forend that has been pillar bedded should work well with a bipod and still allows you to be portable/Harley/varmints.
What part of the state do you live in?
My partner and I hunt elk and sometimes deer every year in Colorado with our specialty handguns (using XP's, MOA, and a Striker). About 9 years ago I did use a 338 Win Mag Encore handgun one year for elk, but other than that, it is XP's for me.