Except for the fact that you specified a lefty bolt action I would very highly recommend 6.5 Swede. Lefty bolt actions in that caliber are rather hard to find. I looked for just such a rifle for Mrs Sumpnz, but came up empty (at least within my <$650 budget).
I've just taken delivery of a CZ 550 in that caliber. With the set-trigger it is sweet. Can't wait to sight it in this weekend. Course never mind the lefty issue that particular gun fails most of your criteria. It's wood stocked, blued, and has a long (23.5") sporter contoured barrel. And calibers like .270 will be flatter shooting, but as you said, reducing recoil is a higher priority.
The advantage of the 6.5 Swede vs 260 Rem is that the Swede can handle up to 160 grain bullets, whereas the COL limitations of the 260 top you out at 140 grains. That and the Swede can get higher velocities assuming you're using a new, or excellent condition mil-surplus rifle (old/poor condition mil-surplus rifles should obviously be treated more gently). The Scandinavians used the 160 grain pills to drop many a moose, so it certainly a very capable round. But the 260 may be easier to find in a lefty bolt.
With any luck I'll be posting about the performance of Speer 120 grain HotCore bullets launched from the above mentioned CZ 550 on Mule Deer. Expected range will be 100-300 yards. We chrono'd those loads from my 1896 Swedish Mauser at 2914 fps (temp was 100F). I imagine velocity will be a bit less from the CZ on accound of it having 6" less barrel and being about 40-60 degrees cooler while hunting, but I don't think I'll loose too much. I'd guess I'd still get at least 2800fps, with most of the drop coming from the cooler temps.