Yes, re-shaping the heel area of the blade should work fine IMO. Provided you know what your doing.
As for the Swiss cheese bevel edge of the blade, I would just hone with a lower grit hone and see if you can find clean steel
Grant
+ 1 to what Grant said. That should be your first move. Until you find that the bevel won't fall apart as you hone there is no point in reshaping the heel. Good luck with it.