I have a similar rifle that is fairly heavy and doesn't get carried much for long hikes or in steep/rough terrain. It is my custom LH Rem 700 in 338-06, and it weighs 9 lbs 11 oz scoped. They built the barrel with a heavier contour than what I requested, but as they had the custom stock inletted for the heavy barrel by the time I saw it, it was too late to change. The kicker is that it shoots and balances so well despite the weight that I am reluctant to mess with it to lighten it up (fluting the barrel and hogging out the stock.) So I use it where I am not in terrain as described above. Love the cartridge and rifle (except for the weight).
Have you considered a 358 Win in a lighter rifle? (Or a 338 Federal?)
As it may just fit your hunting style, and environments, a shorter barreled rifle in a lightweight stock might still provide you with what you are looking for and be one you do "fancy", with great on-game performance.
I have had such great experience with my BLR in 358 over the years that I finally built a LH Rem 700 in 358, to have one in a bolt action. While I did get a nice wood (AA Claro) stock for it, and as the donor had a 22" McGowan barrel, it is heavier than what you want, but a lightweight synthetic stock, and lighter contour barrel (or carbon fiber barrel) would make a lighter rig for you. With a lightweight contour barrel, you would be able to still have irons installed to fit that desire.
I did rebarrel a LH Sako 85 Finnlight II with a Wilson thin profile carbon fibre barrel in 338 Federal. The factory action and stock are not the lightest out there, but have all the features I was looking for. While you may not think that 8 lbs 6 oz is light scoped with a VX-6HD 2-12x42 illuminated B&C reticle, and a magazine full of 5 rounds of ammo...but for me it is lighter than many of my other scoped rifles with full magazines. (And I have packed it in the mountains and shot a stones sheep with it last year, but as it was a day hunt, my pack wasn't as heavy as what you typically carry during your hunts.)
As we continue to age, we usually are not getting stronger and there is a great appeal to carrying a lighter rifle.
There is a line where weight crosses the line for achieving steadiness when trying to shoot accurately with increased adrenaline levels or heavy heart rates and breathing from excitement and/or exertion in achieving reaching the desired shotlocation.
The key is achieving both desires in balance.
Hope you find yours!