Yes, I am going through all of these things, and did speak to the tech rep for the hosting service, who was very helpful.
He suggested that in place of "localhost" I try the actual IP address of the server. This also fails for the same reason. A more specific error message from ZP now appears:
Zenphoto encountered an error
MySQL Error: The database is connected, but MySQL returned the error Access denied for user...
This particular host assigns users for MySQL databases by appending a username to the main administrative username for logging into the hosting admin panels, thus:
mainuser123_dbusername@localhost
There is only one user for the database, amd if I go into the MySQL control panel for this host, and that user is shown as:
mainuser123_dbusername
But I still cannot get in using this info. I am trying to fix this by editing the zenphoto.cfg file and uploading it to the site, but somehow I still have not specified my info in a way that ZP can install.