Lightweight rifles are really a different deal from heavier rifles. While some level of bench and prone accuracy is necessary, in more common usage practical accuracy standing, kneeling, and in expedient field positions (per Cooper) is more important. For me, this means using a sling and lots of practice. The quantity of practice required tends to suggest a lighter recoiling cartridge.
With enough practice, I can eventually get pretty good with a wide range of stock fits, comb heights, scope heights, and rifle balance. But I get there more quickly with a rifle that fits and balances well for me in the first place, and what works well for me may not be what works well for you. You also understand better than I do what tradeoffs you are willing to make between inherent accuracy (from a bench), practical accuracy (shootability), and light weight.
As an instructor/shooting coach, I have noticed that the fit and balance of a light bolt action preferred by shooters coming more from an AR-15 background in practical accuracy is a lot different from those coming from smallbore is a lot different from those coming from a Marlin lever action is a lot different from those coming from a Rem 760/740.