I'm running the most recent stable release, v1.2.
I removed the AddType line from my .htaccess file, and the script runs just as well-- or shall I say, just the way it did before I removed the AddType line.
So now I have "run php as cgi" active, and my .htaccess file does not have the AddType line, and my albums are still returning a "non-existent" error.
Over at the coppermine forums, they suggested I try initiating Coppermine's "Silly Safe Mode". I'm off to try that now...