Zack --
You've got an odd phase shift in your model response. Actually the model lines up pretty well with the precip data -- low in winter and larger in summer. I'm curious as to why your observed flows decline over the summer, when the precipitation is ramping up. Perhaps it is your ET, as you note, but ET is also driven by precip (the more precip, often the more ET because of easy water availability. Temperature isn't the only factor driving ET.). You might try calculating a 30-day moving average (or sum) of precipitation (to smooth that signal) and see how that lines up with your observed flows. Perhaps my eye-ball estimation of what the smoothed precip record looks like (low in winter, high in summer) is not accurate.
An obvious thing to check is to make sure you haven't got the dates wrong for your observed flows (or precip), by several months. I realize this is not likely -- but all of us have made such errors before.
Finally, you might change the GW_DELAY parameter. This could shift the phase of gw recharge a bit. If you increase the parameter (its default is about 30 days, I think) it tends to smooth out baseflow and reduce seasonal swings (ups and downs). If you reduce it, it could increase the amplitude of seasonal ups and downs. I'm not sure if it will change the phase of the seasonal signal or not. Maybe, if you're lucky...
Good luck,
-- Jim