The only solution I can think of that may work is to make the My Account menu a normal menu item within the main menu and then use relative styles to hide the label and show the icon for it.
This would not be applicable to all use cases but for this case it may work.
Unfortunately due to the lack of background image support for relative styles, adding the icon dynamically is not currently possible using that approach.
Also, because each menu item doesn’t have a unique identifier, even if we could add a background image, we would have to rely on the item index in the relative styles to be able to target individual items, which is not ideal for dynamic menus with items that are shown and hidden based on whether the user is logged in or not.