The short answer, unfortunately, is no. The $100-$200 price range is likely to get you a good print scan if you know who to ask, but it’s definitely not enough to buy a dedicated scanner to do it yourself. Lasergraphics’ ScanStation units are fairly popular for this sort of thing, but the most “affordable” option is a whopping $50K, minimum.
I would pay close attention to the Kinograph website as the year goes by. This is a do-it-yourself 16/35mm film scanner that already has a second, improved model currently in development, the ballpark cost of which will be somewhere around the $1K-$2K range, I believe. With that, you then have the option of buying the same area imaging sensors that ScanStation and the like use for their units, if not better. Sony, for example, just released the Pregius 6.5K CMOS area scan sensor sometime last year, and it was reported somewhere on Cinematography.com that Lasergraphics was already testing it for future use because of its improved dynamic range and noise levels.
From what I understand, though, and somebody please correct me if I’m wrong, you won’t pull that much information off a release print by scanning anywhere above 2.5K resolution. Where a larger resolution scan succeeds, if memory serves, is in the amount of noise (or lack thereof) that it captures—- usually the lower, the better. Then you can downres to 2K resolution and still have a fairly sharp transfer with little to no distracting noise levels. But it’s only one of several factors; in the most general/blanket sense, if the camera you’re using also has large photoreceptors, regardless of what resolution you’re capturing in, then you collect information with less noise problems. You also want to make sure you’re using diffused lighting, which can do a great job hiding some really nasty surface scratches without having to perform a wetgate scan.
Hope this helped in some way, and that others with far more experience and expertise in using and building film scanners can chip in here, too. All the best in your preservation efforts! =)