You can implement an actual Windows Gadget using WPF by creating an XBAP. Just add a gadget.xml file and an .html file that contains only an IFRAME that loads the XBAP. That way your WPF application will actually be a gadget and will automatically follow all the rules.
Another option is to use Windows Sidebar Styler. This requires additional software to be installed alongside yours but also allows you to do things you can't do inside the XBAP sandbox without code signing certificates, user authorizaiton, etc.
A third option is to create a gadget that uses something recognizable in the HTML (such as a particular background color), then when your .exe starts up, scan for a hWnd under Explorer that has the attributes you are looking for, inject yourself into the Explorer.exe process, and set your window as a child of it.
A variation of the third option is to not inject into Explorer.exe but rather maintain your Z Index and location (using SetWindowPos) to track the Z Index and location of the hWnd you found.
So many choices...