Update from the other dev:
I was able to replicate the exact same problem on a Siteground dev site and fix it there. It works fine on that dev site and also on localhost now. On his site there are no errors, and I have the compression enabled, but it?s not actually putting anything in the cache folder of his site. I think he has something blocking it or he has kind of server or site cache enabled so updates are showing on his site. As of now I have it working in two locations, so this comes down to something in his environment preventing it from working, but no error messages should be showing. I would maybe ask him to copy over vertex/compression/ to his live site to see if it works there with any server/site cache completely disabled.
I have updated the
Vertex Upgrade Patch with the fixed files; but as he said, if there's something on your server that's preventing it from writing the cache files, the caching won't actually work.