i don't think that you need a longer stem. if anything, a longer stem may increase your chance of locking your elbow. it's not surprising that you have sore hands after a "long ride" on your flat bars. would you consider flipping the stem to raise the handlebars for a more upright position? more upright means more weight on the saddle and less on the arms. just a guess from me. maybe your handlebars are a tad low and that is why you lock your elbows to reach them. your weight is supported by: (1) butt (2) legs (3) hands. the harder you pedal, the more weight goes on the pedal which propel your weight up. if you mess around with the stem make sure not to overtighten the bolts. if you purchased it from an lbs they should do basic fitting free of charge imo.