Re: cut my barrel down?
Your rifle, your choice! You'll lose a little velocity out of this, but probably not enough to make a huge difference in the field. It may well balance better for you, but there's also other ways to change that (stock weights, etc.) if you need to. Depending on the use here, I'd probably try to redistribute the weight in the butt first, and go to cutting the barrel as a last resort.
Again, no matter what anyone suggests, it's ultimately your choice.