I had no idea that there were humans with 4 cones. Amazing!

I hadn't heard about reindeer's anomalous UV sensitivity, however G C Huth's theory instantly comes to mind as a possible solution; briefly, he supposes that it is the size relationships between different cone types that resolves colours, rather than the absolute cone sizes themselves.

Although in this case, presumably the UV sensitivity is unexpected as a sufficiently-small cone is absent; hence a doubling-up of even the smallest cones would seem just the opposite of a solution. Still, if no sufficiently-small structures are present, then the 1:1 cone:wavelength paradigm is nonetheless suspect..