Upstream cache clear issues
I'm not familiar with the term "upstream caching / caches." I'm assuming it has something to do with edge caching... which I definitely suggest you look into; regardless of host service.  I've seen many odd occurrences because of edge caching.

Also try any of the following:

check file permissions for the ability for your web server to write the JS/CSS that it's generating.
Look in your sites/default/files or site/[site]/files directory for css and js subdirectories.  Check the permissions on those two AND delete the .css, .css.gz, .js, and .js.gz files in them.
truncate (with discretion - backup your database) all tables with a _cache at the end of them.