Will it get that much better if I change it?
Let me say, I really, really doubt that changing stocks is going to drop group size. Assuming that your rifle really is a 1 MOA rifle. And that is a big question, for how many rounds did you fire to determine it was a one MOA rifle?
What I have seen, in what has to be a thousand posts, are shooters who shoot a three or a five shot group, shoot a whole bunch of three shot or five groups, one of them is sub MOA, (by random chance), but the shooters claim that because one of them was sub MOA, the load and the rifle is sub MOA.
In these 270 round targets, there are lots of three shot and five shot clusters, some sub Half MOA, if not bullets in the same hole. But, neither the rifles nor the ammunition is sub MOA.
Now this shooter is a former National Champio, winner of the 1000 yard Wimbleton Match. .If he claimed that his rifles and ammunition were MOA or sub MOA, these 20 shot groups would add great credence to his claims.
These were fired in NRA Highpower competition, on a reduced 100 yard range, all shots with iron sights, fired prone with a sling, single loaded, one shot at a time.
Anyway, so much for small sample statistics. I do have a M70 PBR in a Hogue tupperware stock, and you know what, it shoots good. Now shooting a little less than 2 MOA at 300 yards would be considered beneath the dignity of most Keyboard Commando's, but you know, that is not bad from a stock box rifle in a Tupperware Stock. I have not bedded this rifle, which I consider remarkable that it shoots this well as my experience with factory rifles with factory bedding has consistently been disappointing. The only reason I can see valid for monkeying around with success would be if the stock did not fit, or did not fit my purposes.
If your rifle is truly shooting MOA, don't change a thing. You don't know how lucky you are, go buy a lottery ticket for you sure have the luck, and don't mess up a good thing chasing after rainbows.