[Theme: Twenty Fifteen] Header image that spans the site

I like the vertical menu of the default Twenty Fifteen theme, and haven’t found a plug-in that can provide it.

I thought I’d try my hand at creating a modified child them for Twenty Fifteen, but have so far been stymied, so I’m breaking it down into smaller chunks.

1. I’d like to have a responsive logo or header image that sits at the very top of the page, across and above both sidebar and main content. I’ve read and tried the php and CSS revisions here.

I’ve managed two things:
a) a logo that sits on the sidebar above the title – this looks good on small screens, but shrinks on big ones.
b) a logo that sits above both sidebar and main content – but
i) it’s not at the top of the screen, so it looks ghastly,
ii) it seems to have brought along its own menu, so now I have two.
iii) when site opens, the sidebar menu hides down below, and only works properly if I go to the bottom of the page and come back up.
My site: https://50.87.248.207/~metaphp8/

Question
Where should I put a fixed image so that it spans the entire site, at the very top?