Welcome aboard.
I understand what you mean regarding cutting into a nice rifle. That would be my last resort. You might give Grice a call and ask if there is a shorter stock available for you rifle. The last time I was there, in the far back room where the clearance guns are displayed, there was a wall full of aftermarket and factory stocks. I'm just taking a wild guess on this, but perhaps a youth 870 stock would fit.
Grice regularly features limited run Remington's. They are beautiful rifles. Should there not be a short stock available, perhaps they can set you up with a used stock from a regular model that could be shortened. That way you could restore the limited run model to its original condition should you need to. Its sounds as though you've not shot the rifle yet. It would be a shame to hack up that factory stock then determine you don't like the rifle.
If you do have to resort to having the stock cut, I would locate someone who could make it look like a factory job.
Good luck.