Thank you for the very helpful tips! I now clear the cache from another tab in my browser on the www.myExtensionAssetsServer.com page after every modification to my server code and the modifications show on the Twitch Extension in my channel!
I thought at first that I could clear the cache of the pages the Extension was getting from my server by simply clearing the cache of the Twitch channel but that was totally wrong.
Sorry for the very very late response and thank you again!