Well then you could always just go a custom gun route. Buy a Rem 700 action, a Douglas or McMillan blank and an after market stock. Have a 'smith fit cut the chamber and fit the barrel to the action, maybe tune the trigger or put on a Timney if you really want to be custom about it. That kind of rig should fit in your price range. The bipod is a pretty standard item, just attach to the forward sling post and go. If the stock is already pretty much fully inletted (assuming wood primarily) then glass bed it yourself with either a free floating or semi supported barrel. I think a fluted or semi tapered barrel will still give you good rigidity and lighter weight than a full bull barrel.
This really isn't much of a tough job for a good gunsmith and will get the rifle you want without having to go full price for a stock one then modify later on.
