How about a hybrid: Hamburger menu-type icon in the header, but it's just a URI fragment that points to a tag in the footer. Clicking it will just jump the vie

How about a hybrid: Hamburger menu-type icon in the header, but it's just a URI fragment that points to a tag in the footer. Clicking it will just jump the view to the footer, which can be designed to fill the entire viewport on mobile so it looks like what people have come to expect from a hamburger button. An ambiguous up/back arrow will jump the viewport back to the header. CSS can be used to make it look like it's fancier than it actually is, without resorting to javascript. Jumping back won't work great for sticky headers, but that's a feature since it means you'll be less likely to use those awful sticky headers.