Hmmm, interesting problem. You definitely want to resolve it before you go, though - no extra stressers needed on the trip. I guess cutting the elastic and adding a piece would work, provided there's enough additional fabric in the hat itself to accommodate the added size.
Or you could try stretching in by putting it over a round object a little larger than your head (maybe a bowling ball?
) for a week or so, to see if that relaxes the elastic enough to make it comfortable on your head. If the problem crops up on the road, tie a bandanna around your head first and then place the hat resting on the fabric, rather than your skin - that might distribute the pressure a little more, and at the very least would prevent the little hat lines digging into your skull.
If all else fails, buy a new hat.