LÖVE

There are functions available for getting and setting text from and to the clipboard, but is there similar functionality for images? If not, is there a hacky way to do it?

Well, you can make it work at least one way, from löve to the clipboard; there's a function to convert an image into a string.
That said, it may contain chars that aren't printable so it may or may not work.

That said, i think at least windows has separate clipboard space for different types of data? Not sure if SDL'd be able to access the non-text ones :v