Create a menu like the fitbit menu for my wordpress website (can be pure HTML+CSS+JS)

I'd like to mimic the style of the fitbit website menu within my wordpress website.

The website runs on the salient theme from themeforest. However, I'm a web designer so I'm comfortable editing HTML to update the menu if you feel that this can't be achieved with a plugin.

I have a child theme running on a development clone of the website for testing/building.

The menu needs to:
- mimic the way that the products submenu behaves as well as the general layout (full rows + split columns)
- display full width
- Show parent menus with a '+' to then display the child menu items
- the menu will need to load from the current burger icon (or a version of it if you are disabling the wordpress menu system)
- work the same as the example website on both mobile and desktop
- be editable in some way (I may need to change the columns, remove rows, change menu items etc etc) - as mentioned HTML/PHP is fine for me to edit but I'd appreciate a little run through from you when finished

The menu you build doesn't have to link to any LIVE pages, in fact it doesn't need to represent our website at all. I would be happy with a fully editable version of an exact replica of the fitbit menu so that I can design the look to fit within our needs.

I've added so screenshots of the fitbit website but it's obviously better to browse yourself so that you get a feel for the way it behaves.

I personally feel that the best method would be custom code to avoid the use of a plugin (and it's constraints) and to get the exact same look as the example. However I'd be interested to hear how you would tackle this :-)

I haven't set a budget but we're realistic about costs for achieving the above.