If you want to reduce recoil, the best way to do that is with a muzzle brake
. Most serious long range shooters put brakes on their rifles. Reducing felt recoil is one reason and another big reason is being able to stay or get back on target quickly.
Killing deer and killing elk @ 1000 yds are two different propositions. The bigger the cal and bullet the better your odds of a quick uneventful kill on an elk. You already have your 1000 yd elk rifle in the 300 RUM, depending on bullet and load. Are you getting tired of the recoil? If so, I would recommend a brake.
Going lighter is going to reduce your "killing effectiveness" at longer ranges. Not a big deal on dear but something to consider if elk is the game. So what I'm saying is, if you want to reach out and touch, you have to pay the price, in more ways than one. No free lunches. It comes down to improving or decreasing the odds.
So chamber wise, for deer, a 6.5-284, 264 Win, 270 WSM, 284 Win
For elk, a big 30 (you already have one) or 338.
For long range work, I would put a brake on all of the above.
My preference in a production rifle would be a Vanguard or Howa followed by an M70.