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Just to add more info: what you need to edit is the theme.xml file and is under the <dimensions> and <font> tags. I guess you'd have to double or triple the values to make sure everything is visible in a 4k screen.
As for the icons you could try upscaling the image sheet.png by 3x or 4x using nearest neighbour as scale method. ^^ 
Good luck and if you end up managing to do something you like, please share with us, I'm sure there are people with similar setups that would be happy!

(+1)

Thanks for pointing me in the right direction! Looks like this'll take a little while, but I'll give it a bash. :)