Fixes T13273. This element is a bit weird, but I think I fixed it without breaking anything.
The CSS is used by project hovercards and user hovercards, but they each have a class which builds mostly-shared-but-not-really-identical CSS, instead of having a single View class with modes. So I'm not 100% sure I didn't break something obscure, but I couldn't find anything this breaks.
The major issue is that all the text content has "position: absolute". Instead, make the image "absolute" and the text actual positioned content. Then fix all the margins/padding/spacing/layout and add overflow. Seems to work?
Plus: hide availability for disabled users, for consistency with D20342.