If you post your recipe it might help with a diagnosis. Some possible reasons for a soap being lye heavy would be:
-- the recipe wasn't run through soapcalc to get the correct amount of lye and water (or other liquid) to use
-- the recipe was correct but you made a mistake in weighing the lye or water
-- you didn't weigh your ingredients
A rebatch would be difficult unless you're pretty certain how much extra lye (if any) was used. I've never done what Mommysoaper is referring to, but I know Kevin Dunn is an expert so I would believe what he says about lye heavy soap reaching normal levels after a time. I've read that in the "old days" the soap maker for the family would make the soap and let it cure for a year before using so they were sure it was not lye heavy. They wouldn't have had precise scales we have access to or whatever - but by putting the soap up for a long cure the soap didn't "take the hide off" like the fresh, lye heavy soap would have.
As far as the crumbliness of the soap - it could be lye heavy, but I've had crumbly soap if I've had it in the fridge or freezer and I don't give it long enough to come back to room temp before cutting. I now make myself wait at least 24 hours after removing it from the fridge or freezer before I cut.