Hi @SLIS, I've not seen any specific issues with W3 and this plugin myself thus far, just a couple past issues that were actually related to the smush.it service instead.
To include images here you can post them through any service like Google Drive, Dropbox or screencast.com. You can simply provide a link to the images that way.
Layzloading plugins should work just fine alongside the plugin, it handles the smushing of the images before they're ever loaded on the page, so there should be no problem there.
With the debugging enabled, you should see any relevant errors displayed on the page when attempting to smush images.
Your screenshot should help us to see the smushed status of the images. But I doubt that's actually an issue given what you've just said.
That said, have you tried deactivating W3 caching and testing with gmetrix?
Looking forward to seeing this sorted for ya! :)