That last paragraph is rather strong... There are people with far worse conditions than smelly feet.
I would suggest washing your feet scrupulously (with a bath brush) morning and night. And never wear shoes without socks.
I had a similar issue after wearing shoes with no socks on a warm weather trip but only in one shoe! It seems that some stinky fungus must have 'invaded' the one shoe. I threw out the insoles and I guess it was in the lining or leather of the shoe because it didn't disappear.
I suggest freezing the shoes for a few days and hopefully that will kill the fungus. And because you suffer from hyperhydrosis, never wear shoes without socks.
It seems like a no brainer...