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1. Tires: You don't need to swap to skinnier tires. You can get wide, smooth(er) tires and that will improve your ride a bit. Also, wider tires offer more cushion from surface imperfections (like potholes).
2. Handlebars: The guy at the LBS was right- swapping to drops will get pricey in a hurry, especially if you pay them to do it.