Does Puddles have other behovioural issues? Has he always been like this, or is this a recent development? Does he scratch at his kyit once he's dropped it, or does he just saunter off and ignore it?
It does sound like you've tried all the reasonable things to try. Other than maybe, which might be tough if you are in an apartment, separating him from his brother in his own room with exclusive litter box in case he doesn't like to share. Then, once he's marked it with his scent sufficiently, letting him out.
PS: Also, if he still has his dude bits, get him neutered. That often helps with male cats' territoriality and general disposition.
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Better educated sadness than oblivious joy.
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