To pay a shop to do all this definitely doesn't make sense, just buy a road bike. If you do the work yourself, it's a lot more reasonable.
Getting a frame painted is not that expensive, but the labor to strip all the parts off and then rebuild is. As for turning it into a road bike, it depends what you want to achieve. Switching to drop bars will be fairly expensive. You'll need at least stem, bars, brake levers, shifters, new cables, and bar tape. It's a fun conversion to do, but I don't know how practical it is.
If what you want to to make the bike you have faster, I would get a wheel, put on narrow high pressure slick tires, cut the bars down a couple inches (maybe a longer stem), replace the chain and cassette since they're probably worn out, new brake pads, cables as needed. Rattle can paint job for looks. You could easily spend $200 bucks doing that, but you should end up with a quick durable bike. (A big question is if any of the bearing races need repair/replacement - give the bike a thorough check over before you start buying parts.)
As an alternative to drop bars, think about getting something like this (
http://store.velo-orange.com/index.php/components/handlebars/vo-montmartre-handlebar.html) and mount them upside down. You get a dropped aggressive position, but can use your existing parts, and end up with a really unique look.