I don't think Epicurus viewed it as helpful to see things in such black and white terms
Totally agree, with all of this post. 
Critique of the Control Dichotomy as a Useful Strategy
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if someone things that "I can't have any pleasure, or any happiness, at all so long as I am experiencing any pain," then they have set themselves up for failure.
Well put.
Along those lines, Epicurus himself was experiencing severe pain in his last days but could also call that time blissful (μακαρίαν "blessed" aka like a god) and could experience the pleasure of the "gladness of mind" (χαῖρον a kinetic pleasure). That seems to me a perfect embodiment of what Epicurean eudaimonia encompasses.
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