Lighten up the rig is easy, Go with a 22" sporter.
I know "Velocity loss", "So and so on the internet said", " It will limit your range", Blah Blah Blah.
Yeah they say the same about the 25-06, the win mag and every other overbore cartridge but the reality is that 22" sporter barreled hunting rigs probably kill more game on the planet every year than all the other longer barrel lengths combined. I have a 22" 25-06 that has been piling up whitetails for many years despite what the internet says about needing a 26" barrel blah, blah, blah.
As for me, The last build that I'm really proud of and feel I made the biggest improvement to is a model 11 I cut down into a little 16" barreled .308 carbine. Nothing want's to find itself in the crosshairs at any reasonable range. The improvement to the ease of carry, portability, pointability and general handiness and feel of it is simply amazing.
Just a friendly word of advice to not over think this and to help put what you read into context.
Those that write it aren't gonna carry your rifle for you and the game you shoot isn't gonna tell you your barrel is too short or thin.