I sort of found a way to do it. Not exactly what I wanted, but it works just as well.
Create a folder somewhere (under My Documents or wherever. Doesn't matter). Create shortcuts to your Office programs and place them in that folder. Right-click the taskbar, go to "Toolbars" and "New Toolbar...". Select the folder that you just created. Now, when you click the arrows by the folder name, your Office apps pop up.
Again, not an icon, but just as good. I would suggest making the folder name short (Office or MSOffice, etc.) because the full name is displayed on the taskbar. This is especially important to save taskbar space (I have tons of icons too, 18 at the moment). Another problem with not being an icon is that an icon will appear when you start it, which may cause problems if you have the taskbar completely full already, but it's something that I don't mind dealing with. If you haven't done so already, make the taskbar smaller (room for tons more icons!!). Hopefully this is something Microsoft adds in the future.