Frederick,
This (catastrophic) issue has been reported several times in various forms and is so far not addressed. It is not a permissions issue. It is an error in the script in locating the cache directories on the host server. Your method only works with some standard host configurations, but fails with others.
Anyone having problems with minification can easily test this by hard coding the cache paths and document roots in the following files:
MinifyAdmin.php $cache_dir
TotalCacheAdmin.php $document_root
CdnAdmin.php $document_root
MinifyAdmin.php $cache_dir
PgCacheAdmin.php $cache_path
and presto, Total-Cache magically begins to work. I have since dug around other core files and it looks like the error is likely affecting the entire plugin.
Having users hack around core functions is not a good idea. Assuming you are unable to fix this any time soon, can you please suggest where a better point is to hard code these paths so it is picked up by the entire script.
Thanks much