I'm going to try to offer an out-of-the-box solution and suggest a remote-controlled quadcopter / octocopter UAV with a camera mounted on it. Such a system seems to satisfy most of your stated and implied needs:
I'd have to rent the plane and the pilot and I'd like to keep the price down as best as possible.
A UAV seems like an excellent choice in this regard: unmanned vehicles tend to be cheaper than manned ones, and don't require a pilot's license to operate (although other regulations may still apply).
You probably do still need a skilled operator, since controlling a quadcopter does take some practice, and it's difficult (not to mention potentially dangerous) to control the vehicle and the camera at the same time. Having a separate pilot frees you from having to do that job yourself, and lets you concentrate fully on taking pictures. The commercial operators I know of that do this kind of work always have a separate pilot and camera operator.
- Good view of the ground, though it doesn't have to be straight down (I'm not doing surveying). [...] Big windows. [...] Also, a high wing is probably preferred. Though, if it's exceptionally good at holding a bank, it may not matter.
Check. The setups I've seen usually have the camera mounted under the vehicle body, so you can point it in any direction, including straight down, and the only things that could possibly get in the way are the landing struts.
- Stable while banking so I can more easily track shots when the plane is at an angle.
- Ability to be held stably at a bank without actually turning the craft, again to help me track my shots.
Check, sort of. No, the quadcopter itself can't maintain a steady tilt without accelerating, but the rigs I've seen let the camera be held steady at any angle, while the copter can freely move in any direction in three dimensions.
- Low vibration, for the same reason as stated over the last two.
Check. At least, I've never heard of this being a problem.
- Can fly low and slow for if I want to get close to things (within reason.)
This is the one aspect in which remote-controlled helicopters absolutely excel: they can hover in place, or move at any desired speed (for panning shots), at any altitude above ground level. Want to hover in front of someone's face to shoot a portrait of them? Perfectly possible (if maybe a little bit unnerving).
Mind you, I haven't actually flown or worked with such systems myself; most of my knowledge comes from watching a demonstration at a "maker faire"-style event by a local company operating such systems, and exchanging a few words with the folks there. But it was definitely impressive, and the way I would go if I ever needed to do some aerial photography.
That said, there certainly are also some photography applications for which remote-controlled vehicles are not so well suited, such as high altitudes, very long flight times, flight over significant distances of inaccessible terrain or operation in bad weather. However, if your requirements don't include any of those, they may well be much more practical and less costly than renting a manned aircraft.