After reading some of those links and fiddling around a bit, it dawned on me why the prints look so different. If I turn on gamut warning and adjust my saturation under the WHCC profile to bring it within range, it looks exactly like the print. If I then switch to the Epson proofing profile, it still looks the same. HOWEVER if I undo the desaturation, put it in the Epson proofing, and turn on the gamut warning, it's still within the range.
So basically, the Epson can print to a wider gamut than WHCC. There's nothing wrong with my screen.