Change TPopupMenu.BiDiMode of just one TMenuItem's submenu?

Question

I have a TPopupMenu that acts as a tray menu (it is linked to a TTrayIcon). The .BiDiMode of this menu is set to bdLeftToRight, and this is how I want it for almost all its items.

But I have one TMenuItem as a submenu. I want this menu item's arrow to be visible on the left side and the submenu to be opened to the left. Also the potential image should be positioned to the right side of the item. Of course, I want this to be applied to all its children in the submenu, too.

Reason: the popup menu is fired near the right side of the screen, and the submenu opens to the left but the arrow is to the right.

This type of behavior can be achieved if the .BiDiMode property of the menu is set to bdRightToLeft. But the problem is that this is applied to the whole popup menu, and I want this to be applied just to a menu item and all its children (in the submenu).

Is this possible, is there some sort of a hack to achieve this? Or maybe to ownerdraw the items to achieve this similar behaviour?