The limit applies to the length of the string that you use with show_motd(). Showing a webpage is the only way that I know of to show more data. In this scenario, the webpage (e.g. PHP) does all the queries to Steam and generates the HTML. When using this method, there isn't a limit on length.
You might be able to send all the low level data in a URL (via GET) provided that the URL remains under 1536 characters. Then, your PHP script can get the avatar and any other data from Steam.
As mentioned by JocAnis, some people actually have access to the stats database from their web server so they can do everything from the PHP script and you just send the simple URL without any parameters.