Of the choices you provided, only the 35 whelen fulfills all of your criteria. The others are either not suitable at further ranges or compatible with te BDC scope, or factory ammo is not readily available.
There are a bunch of other rounds in he non-belted mid power range (Winchester short magnums come to mind) that would fulfill this as well. None have the longetivity the whelen does, but a 325 has better bullet selection available. The 35 has always been a step-child caliber when it comes to bullet selection.
A 385 ruger would be a the upper end of this spectrum. If you were considering a 45/70, the 375 is comparable in recoil.
I somewhat disagree here,,, Really the BDC scope is a non issue out to 200 yds, with the exception of the slower rounds in which he would have to figure out the calibration for them. But,,,as they have mentioned before,,,what concerns me the most, is the mention of "short mags". TC does not chamber them nor recommend them in the Encore. They can be used if loaded down, but have been known to stretch frames with factory ammo.
Factory loads for either the .35 Whelen or the .338-06 and the rest of what was questioned, chances are wouldn't be readily available. Except the most well stocked gun shops or chain stores. More than likely, they would be special order or bought over the net through a supply house such as Graf's or Midway etc.. So for me ammo is a non issue also. The Whelen may have a better selection of commercial ammo, I'm not sure I haven't looked. But, the for the handloader if he chooses to do so, the .338 caliber has a wider selection bullets. There are however enough quality bullets and ammo for either caliber/chambering suited for any NA game animal.
But for the most part with the question stated, I could be happy with either the .338 or .35. just I feel the .338-06 has a little, however slight versatility going for it.
Dave