i don't under stand the thick ear? i injected ears a couple of times. moved the glue around and clamp. haven't had a thick ear i could see.
If you have a true drumming issue and either don't rehydrate and move skin around or slice skin and fix as stated above, but just inject glue, I find it hard to believe that if you try to flatten that area down to the liner, that it won't eventually drum again. Now, if you inject the glue to sort of fill the void created by the drumming, you might be able to minimize the drumming but it would also be thicker there due to the layer of glue being used to fill that void.
Of course all this depends on the size and amount of drumming trying to be fixed