We have a Glacier Bay Flapper-less toilet - the kind with the bucket inside the tank that fills up and dumps the water in the tank when you flush. When you flush, the toilet fills with water and surpasses the normal level so much that you think it is going to overflow but then it drains slowly until the bowl is almost completely empty.

The flush valve has been replaced but did not fix the issue. Any ideas?

By your description, it sounds like the toilet has a partial blockage in it. Try plunging aggressively when the water is high in the bowl. If that doesn't fix the issue, go out and purchase a CLOSET AUGER tool... see youtube video on how to use:

If using the closet auger fails to fix the problem after numerous attempts, that would suggest that there is an object in the toilet bowl and the toilet will have to be lifted off the toilet flange so you can turn the toilet upside down and remove the object.

Back to you...

Mark