It is only now I had enough time to make ShiftNav working well on our site. You can see it with widths < 1024px.
I had to make a copy of our main menu for ShitfNav, because it turned out to have problems with the "column" elements of UberMenu we are using for megamenu. That was the reason why I was not able to see up to now, how it was working with several levels.
I can confirm now, its shift menu functionality is quite close to what I wanted. The main difference is the missing opportunity to go back directly to previous levels, we have to go through the "back" button.
This is not bad at call, can be accepted, while I hope to see one time a "hide accordion" opportunity in ShiftNav, which would hide any other accordion on the same level when a menu is opened. It should not be so difficult to realize, I made a suggestion to the developer of the plugin to do it.
So, thank you, I would not have been tried it without you.
Would you accept to complement our [url removed, login to view] or to modify the [url removed, login to view] in ShiftNav, to align the look of the shift and accordion menus to the mobile menu design of our site (I guess also a custom toggle is to be inserted in the [url removed, login to view] of our theme)?
If you are ready to do it, please set the budget as you feel it fair, considering of course all the efforts you did already made.