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Fontify org quote blocks with font-locked markup

I have org-fontify-quote-and-verse-blocks set to t and '(org-block ((t (:foreground "#2E8B57")))) to make quote blocks stand out in a particular color. However, this also means that I cannot get markup like /emphasis/ or *bold* to display properly in such a fontified quote block.

So is there a way to have both of these together? In other words, have fontified quote blocks that display in a particular color and have them display text according to its markup (i.e. /emphasis/ looks like emphasis?