I've used W3TC a lot in that past and never had an issue with minify. For complex sites it can be better to use manual rather than auto minify, but I've never NOT been able to get it working smoothly.
Until now 
It seems the rewrite settings ee creates (using site create --w3tc) cause a 404 on any W3TC minified files (i.e. css/js). Anyone else hit this problem and know what to fix?