Sorry, but if you can flex your action in your stock by tightening the action screws, the stock/bedding and pillars are out of whack. There should be no way to bend an action just with action screw tension alone unless the stock/bedding is giving way too.
This IS a very common problem as many rifles suffer from poor or inadequate bedding/support. Most common in stocks that have inletting designed to not need any bedding - alum chassis.
The same idea of bending an action can also happen to a solid bottom rifle if the bedding is bad enough. Just put a solid action into the same stock as the 'bending' mag action and I bet you can create the same problem.
The amount of action flex during the firing process of most cartridges used in precision shooting would be best described as minimal. That is why we use recoil lugs and if concerned, use a thicker one.
An action WILL bend if the barrel hung off it is long/heavy enough AND there is no support given for the barrel. However, the average varmint contour 26" barrel isn't going to stress any modern action I am aware off.
If there is concern about action flex due to hanging a long and heavy barrel off the front, a barrel block is a great idea. However, similar support can be reached by bedding under the first 4 to 6" of barrel - similar in length to the block you would otherwise use.
The difference is you don't have the heat sink qualities of that block.
All you have to do is look at the variety of superbly accurate tactical mag fed rifles on this board. Many are as capable as any F class rifle for mechanical accuracy. They even feed their ammo from the mag.
If there is concern that a particular bullet would sit too far from the throat for best accuracy, just change the reamer specs when building the rifle.
Now you can have a mag fed ammo with the same bullet to rifling set up as any other rifle.
Just don't stick that bullet into the lands. Makes a mess if the bullet pulls out if you need to empty the chamber.
Or you can use a Savage center feed mag and push your bullets out to almost 3" OAL for a short action.
Here is a pic of my test target for my new Shilen 260AI barrel. The Savage action is mag fed.
Read all the details here
http://www.mysticprecision.com/htm/rifle.php#barrels2
Jerry