Choosing a reference frame so that sub 2 is stationary and sub 1 is moving at 17 m/s is a bad move. You get close to the right answer though because the speeds of the subs are very small compared to the speed of the waves. Consider this same system where the speed of the wave is lets say, 100 m/s and you'll see what I mean. Using you're method, you'll get the frequency detected by sub 2 as 1638 Hz as opposed to 1811 Hz using the Doppler method. This should clear up what you're talking about in the second paragraph of you're response too.
Finally, the objective of this thread is to gain some authority with which to challenge my professor who marked my answer of 1423 Hz as incorrect on my midtem exam. ???
I know this thread has been marked "solved". But I just want to make one comment. It doesn't matter which frame you choose to do your calculations, the answer will be exactly the same. If you want to avoid rounding errors, keep everything in fractions.