I would not say the two schools are fundamentally incompatible. I believe in an à la carte sampling when it comes to philosophy, provided it makes sense. I may be naïve.
I think a stoic approach is very applicable when a person is facing situations of responsibility, whereas an epicurean approach is probably more favorable to moments of privacy and friendship.
My gripe with stoicism is my impression that the school emphasizes emotional austerity/asceticism ("freedom from the passions") over emotional engagement with life. I admit it's likely a shallow read of the philosophy.
However, I wonder if a sensory-based embrace and appreciation of life is something fundamentally human that people can miss out on when they overvalue emotional austerity.
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I started appreciating stoicism when I realized the popular conception of it as anti-emotion is a bit off base. In that respect it's sort of the flip side of the point you make about how the epicureans are misperceived.
I believe that "freedom from the passions" is more about not being ruled by your emotions than it is about not having them. The Vulcan line "We control our emotions so that they do not control us" comes to mind.
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