I have in my experiments folder a project file that I used to replace completely the Neutral Menu. I attach it, not for direct use, but perhaps the way I did it could be adapted to the site in question if others don't find a way of mending the Neutral Menu.

The only JavaScript used is in the Footer Code of the container (class="top"), and that is called by the Custom Attribute (data-event-onclick with a value of 'fc()') which is applied to each of the menu items.

It doesn't use the JavaScript that the Neutral Menu does: everything else is done in the styling.

Frank