Luke, I think there is a hack to do what you want - you need to add the non-empty role attribute for HTML nodes that are missing in the TestComplete Objects tree and then they should become available. You can do this by modifying the source code of web page, or by using code like this:
page.contentDocument.Script.eval("(function () { var spans = document.querySelectorAll('span[class^=glyp]'); for (var i = 0; i < spans.length; i++) spans.setAttribute('role', 'button'); } ())")
It finds all the span elements with the class attribute starting with "glyp" and adds to them role attribute with the "button" value.
After this call you should be able to click on these spans.