Per the documentation:
You can use
ChangeHITTypeOfHIT
to update any of the HITType properties of a HIT. All properties except for Reward can be updated at any time.
In short, it is not possible. You have to close the HITs and reissue.
UPDATE (July 2014):
AWS reports on the MTurk developer forum that you can now change the HITType of a HIT to one that with a different reward amount and that the documentation is incorrect.