Why such a big pan? You could do the same thing with a cheap aluminum pie tin. Or go to a goodwill and buy a frying pan.
Adding the hot water to the dye should work just fine. Then just completely submerge the disc, stamp down. (If you go stamp up you are more likely to get air bubbles under the flight plate.) You could put some marbles or chopsticks or something like that in the bottom to keep it from resting on the bottom. However since you won't have heat you don't have to worry about burning the disc so it might not matter.