It will take a long time for the frog to start losing weight from not eating let alone starve to death. Giving the frogs digestive system a break from food to work on moving all that chitin wont hurt. You should put a wet glove on a massage the impaction a bit throughout the day each day to help maybe dislodge it.
Have you been keeping the frog in a bare bottom or paper towel lined bottom with shallow water? My frogs always seem to have an easier time pooping when they are kept in water, and sometimes when I switch them to bare bottom water set ups to wash all my moss they poop within the hour.
Plus, if you use a bare bottom water set up, you will be able to see whats in any of the poop that may show up. Im betting you are going to find lots and lots of mealworm husks.