If you found used drop bars, a seatpost with a little less setback, and a shorter stem, you could put your current shifters and brakes on the drop bars, or at least the shifters and use your existing v-brakes with something like this Tektro RL520 Lever Set. They have the proper cable pull for v-brakes.

Say $50 for seatpost and stem, and you can get the linear-pull levers for $20-50 depending on whether you can find them used and how fussy you are on brands and such.

Much cheaper than trying to convert to actual road components, and would at least let you try out the fit and hand positions. Adjustable stem is an option if you're looking to figure out what you like for a future purchase as well.