Hello and welcome to the site!
I am not a fan of the falling block guns. With that said, a friend of mine has a Ruger number 1 in a 6-284 that will hold 1.5" groups at 400 yards with a Shillan 2" x 30" barrel and lots of fancy loading.
In my opinion, you will have a problem shooting the browning from a bipod unless you can find one that mounts very close to the reciever. Your problem will ley in putting pressure on the barrel.
I think Nikon monarch's are good for the money (34 MOA adjustment), but there are lots of other models that will be right in that ball park such as the sightron big sky (45 MOA adjust) or the Bushnell 4200 or for a couple hundred more the VX III (@35 adjust), and for a few hundred more the Leupald vxIII LR with a wopping 75 moa adjustment).
You shouldn't shim your scope, I've done it and had problems with the scope comming loose under recoil and also had problems with damaging the tube. If you need more elevation, use Burris Signiture rings with shims or find a custom rail that you can put on. Burris sig rings come in the same dove tail mount that Leupald come in (twist in front and fit between in the rear). You can get different sized shims to give you between 10-20 moa of angle increase depending on how far you rings are from eachother. Looking at a balistics cal like JMB, I see you will need to be able to adjust 20.5 inches per hundred to make a hit if zero at 200. You will need a scope with a minimum of 45 moa of adjustment - or suitable shimming.
I used to re-load but now I "hand-load".
-- Well, at least I try