I thought about switching over to downtube shifters, which would address the knee-smack issue. After playing around with a friend's bike with downtube shifters I decided that while they were in a better location than the stem, they still were in an awkward spot to reach.
So, I took a gamble and bought some vintage Shimano bar-end shifters off of a person here on the forum. Let me tell you, this was the best upgrade I've ever done to a bike. The shifters are now in such a convenient spot that inside my first couple of miles I was changing gears without conciously thinking about where the levers were located. I absolutely love the bar-end shifting, and would recommend this option to anyone looking to change the shift location and aren't interested in the expense of brifters.
As a bonus, along with my Tektro brake levers I was able to run all of the cabling under my bar tape, which really cleaned up the look of the bike.