Thanks for sharing. There are a lot of plugins active, making it more difficult to troubleshoot. Do you recall any changes made to your site or third party plugins when this started to occur, this could include any manual updates from when your AMP URLs worked previously?
One troubleshooting step you may wish to perform is to switch temporarily to transitional mode AMP and check for the same issue. Your active theme has an AMP compatibility plugin allowing your jQuery based navigation menu to work in AMP URLs.
If the same issue occurs in transitional mode please share your full PHP error log via an publicly accessible Google doc, a GIST or PasteBin. You can provide a link to this error log using the same form used previously.