[TABOB]

Koozie material is foam. when you heat press or heat belt dryer, koozie will be damaged shape.

That's just the cheap ones.
The neoprene ones don't have this problem.

I recently did an order of 400 koozies only to find out the ink started bleeding on the koozie once they started using them.

What ink and what do you mean by "bleeding".
If the issue is crocking (very common with red inks) then try adding more binder.
That's curable reducer for plastisol, and clear base for water based inks.
Obviously you have to make sure the ink is cured.