Hamburger Menu on Desktop with Shopping Cart

I'm using the following script to change the usual Nav in desktop mode to a hamburger menu - The client has requested this despite guidance otherwise.
 

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I've just added an e-commerce section to the site and when that is in place, and with a shopping cart selected to be in the header, two things happen.

The hamburger menu icon moves to the left of the logo.

The hamburger menu doesn't actually appear in the header.

I know that this is because the script says to hide the header items/actions etc. 

Is there any way to keep both the hamburger menu and the shopping cart in the header on desktop mode.

I've found that using a mobile menu plugin is better than this type of CSS solution to always have the mobile menu.

Does anyone have a solution to this?

15 hours ago, pro said:

Does anyone have a solution to this?

https://www.ghostplugins.com/products/mini-mobile-menu-in-squarespace-71

18 hours ago, Ziggy said:

https://www.ghostplugins.com/products/mini-mobile-menu-in-squarespace-71

Thanks, but I was hoping for a custom code solution, not another purchase on top of what I already pay for Squarespace, which is a lot.

All I want is as simple as this, but no one seems to know how: