Probably 90% of the trouble with an action like that is that it is "semi finished". Combine that with mass produced wood stocks and it should be no surprise that the bedding is not good.
Yes, I would remove about 1/8" of material behind the recoil lug to provide room for a really good strong piece of bedding in that area. Make sure that the recoil lug is not bottoming out ! If you go here Fiberglass Supply- Fillers and Modifiers
and scroll past all the inappropriate fillers for bedding to the "cotton flock" and the milled fiberglass and carbon fiber, that is what you are looking for. Get the shorter fibers for bedding because you do need the stuff to "flow" a little. You mix the resin first, then mix in fibers until it starts stiffening up. Remember, the fiber gives it strength, resin on its own will crack easily ! It will take a lot of fiber and stir it good. I think the recoil lug is the most important area and remember not to torque down the action screws tight when waiting for it to set up.
Then I would go back afterwards and drill and measure for pillars and then install the pillars. The pillars should take the full compression of the action screws. Not sure if a pillar would be possible for the front action screw, I don't know how much wood you have in that position.