those two that you already own you can do a lot of shooting and training for long range, and have a lot less than $1000 spent. You could even upgrade the 257 to a lighter/stiffer B&C stock and likely see a benefit. You have a bit of a tough task ahead of you IMO. Like you mentioned light weight and low recoil are polar opposites. Also, in some ways light weight and LR shooting are competing concepts too. Thirdly, even if you get a good LR rifle you may not be able to find off the shelf ammo that allows you to get the kind of accuracy you need for the LR shots you are talking about. I think you are going to have to embrace the concept of a brake. It really is about the only way to reduce recoil like you need to and still have enough performance for elk at LR. And IMO you have to plan around elk even if it is overkill for everything else just to be sure you get the job done on those magnificent and tough creatures! It sounds like your 7mm is too heavy and kicks too much. Have you thought about having it worked on by a good smith and turn it into exactly what you want? The concern I have for you buying something new is that you don't have any assurance of getting a good shooter and with a limited budget and needing to shoot factory ammo you