mod_pagespeed in general works really well with upstream caches for resources. You can use relatively short (say 5 minute) TTLs on your CSS/images/JS and mod_pagespeed will check back for updates based on that TTL. However it will serve 1-year TTL-resources to the upstream cache & clients, renaming the file based on its content signature if it actually changes. See
https://developers.google.com/speed/docs/mod_pagespeed/filter-cache-extend for more details.
This works perfectly with webp conversion because we rename jpegs to have a .webp extension and rewrite the HTML to point to the correct version based on the user-agent.
We are also working on support for caching HTML in front of the Apache server while supporting webp conversion. We have to get Varnish to be smart about user-agents, which is possible with VCL. Stay tuned as we work out the details on this.