Lefties, look to Europe! besides Sako, you can choose from
Blaser - a real nice straight pull bolt in LH, the model R93.
Sauer -model 202, a turnbolt
Mauser -model 03, another turnbolt.
All three offer interchangeable barrels, which may mitigate the cost of a somewhat more expensive rifle if you plan on owning two or more different calibers sometime.
Heym makes a higher end rifle in LH. Their model 30 is a straight pull bolt.
You may also want to consider an O/U or SxS rifle, of course they are ambidextrous! Merkel, Blaser, Kreighoff, Heym, and many others make them for the European market. They won't be bought for your $2000 budget though.