I would certainly look at the Sako 85 as well as Hill Country rifles. Nosler Custom would also be high on my list. Not sure all of these are available with oiled wood. Most makers these days seem to prefer synthetic.
From what I have heard, the Kimber is kind of a crap shoot right now. Might get a good one, and you might not.
The Cooper's are very nice rifles, and all I have ever been around, and I own 4 of them, are shooters, but I believe that Cooper is having some problems right now. Cooper only has a 3 round mag, but they have extra mags available, so no big deal..
I have had some considerable issues with two of mine that I have not decided whether or not to post about and I know of at least 8 other rifles from my area that have experienced problems.
I would be glad to fill individuals in through a PM, I'm just not ready to publicly disclose all I know right now.
Bill