Hi guys, I had a similar problem, W3 Total Cache was adding a <script> tag with the path for a minified JS and this was invalidating my APM blog posts.
I solved (still waiting Google to display the AMP pages in the search results, anyway from console there are no error but one message that says:"Powered by AMP ⚡ HTML")
My solution was to go in W3 Total Cache > Minify > Advanced > Never minify the following pages and type /amp/ in the text area.
NOTICE: My permalinks are set as "Post Name" so they look like a folder sequence https://mywebsite.com/sample-post/
The AMP plugin by default just add the text /amp/ to the post link, so now every link ending by /amp/ are not minified by W3 Total Cache.
Not a big deal as an AMP page is supposed to be quite small anyway.
Hope this will help.