Boy did I pull my hair out on this one!
It turns out, this time, that a cross-browser problem was NOT Microsoft's fault! It appears as though FireFox 3.0 made a breaking change with the way it dealt with doc types.
If you see your Silverlight apps working in IE, Chrome, but blank in FireFox, try removing the doc type from the hosting .ASPX page:
This obviously isn't ideal, but it works. So if users can install Silverlight properly in FireFox, but the Silverlight control is blank, try this. Also, make sure the latest Silverlight.js file is in your web site's root folder, and the users have the latest Silverlight installed.