I see no problem with your preferred upgrade. I had precisely the opposite done on my mountain bike, a Giant Boulder, and I bought used drop bars and brakes, new stem, and had a local bike shop put everything together for me. They had to re-cable everything, as well as install a stem-mounted friction shifter. I probably have about $50-60 in the whole conversion at best. Shop used stuff and you can save a bundle like I did. I like the more natural (for me) hand positions of the drop bars, as well as the stem friction shifters.
Giant Boulder: $200
Stem: $10
Drop bars $15
Stem shifter $10
Cable & labor $15 or so, as I recall
The above is as close as I can remember. I felt no need to buy so-called "hi-end" while shopping, and I believe you should consider this a low-end estimate of what your conversion will cost. Some bike shops, as well as flea markets, will have piles of trade-ins, used stuff, or new old stock at low prices. I don't punish any of my bikes, rarely going off-rode only far enough to park it. You should, of course, consider your own usage when shopping for components, or you can expect to buy replacements. Forget about that "buy a bike designed for it" ****. Do what YOU want. It's your bike, and you are the one who needs to be comfy with it. I don't see you breaking $100 for this, unless you like really expensive components. I have a $200 Giant for the same reason I have the cheaper Fender guitar....I can't tell the difference between the low or high-priced stuff when using them. Do what works for you.