Well, it has finally happened. I've hit version 1.0 of the Helpdesk Customizations Plugin.
In the most recent version, I've added info for tickets relating to software items and fixed a bug where the plugin would only retrieve 100 tickets in the info bar.
If you run into this problem, here is the code to get around it for now.
tkt_ct = (new Ajax.Request('/api/tickets.json?total_count=true&filter=open', {method:'get', asynchronous:false})).transport.responseText.evalJSON().count;