A good pillar bedding job is always the preferred way to go with a hunting rifle BUT if it is really for hunting at the usual distances for the usual size animals that one select a 30-06 for, the tupperware stock may suffice. Just remember to rest it right in front of the action, if you are sighting it in, and/or working up loads at the bench.
The reason that I say this is that I have seen the very sort of stock that you have give good results at the range.
One day while a friend and I were at the range, a young fellow asked our opinions as to why his rifle a .300 ultramag was giving him groups that were twice as big as before, this with the same factory ammunition that he had been using. When I checked the rifle over I found that the action screws were not tight. I tightened them to what, to me felt about right, and he then tested the result. I should mention that he was shooting off of a bipod, with no rear bag, at what had to be an 8" orange, stick-on target, with no rings. He shot three shots that would literally fit under a dime. It was amazing. No, I don't think that this would be in any way typical, nor would I expect the same result on a subsequent test, but it did happen. Knowing how rare and unusual the group was, I suggested that he retrieve it without adding any more bullet holes, and I signed it, noting the distance and date. Later, I heard that he had framed it and hung it on the wall behind his desk at work.
If you decide to try to improve your rifle's stock situation, I think that the advice that you were given about not spending money on your current stock is correct. On the other hand, if you do the work yourself, given the value of the stock, you have little to loose, and you might improve its performance. The main issue will be getting the bedding to bond properly to the stock. You may want to do some research on the internet on that subject, if you decide to give it a try.
