I have the £150 Sony HQ1 from Dogcamsport. I have done in-flight filming with it, looking forward through the windscreen, but the quality is IMHO very disappointing.
The video is just about OK if reduced from PAL (756x525 or thereabouts, in reality) to 320x240 but there is still a lot of geometric distortion which is
not related to the windscreen - which I suppose could be post-corrected with an upmarket video editor.
Another problem with the HQ1 is that it uses the speed of its electronic "shutter" to control the exposure, and in normal bright daylight the shutter speed is very fast - of the order of 1/5000. This produces really weird effects with the prop, making it look like a 6-blade and going backwards and all over the place. This issue may be solved by putting a neutral filter on the front (forcing the shutter to be much slower) but I did not try that.
Connecting my HD cam's composite output into the video-USB converter yields a high quality video so the problem is not downstream of the HQ1.
I have also tried the best webcam products money can buy and they are no better than the HQ1. Their only advantage was that they have a direct USB2 interface so no video-USB converter (£50 on Ebay) is required.
The advantage of cameras like the HQ1 is that they are waterproof and have a small frontal cross-section so can be mounted outside the aircraft, but the OP's application does not seem to require that and anyway doing that is legally dodgy
I did look at a better quality bullet camera and found a £750 Sony one (plus the cost of removable lenses, so over £1000) which I guess is what a pro would use, but could not find anybody selling it. They must exist...
Personally, I'd buy a cheap HD camcorder; they go for about £300 now and the quality is way way way better than these bullet cameras.
The possible downside of a camcorder is if you need to do a movie exceeding its media capacity. It then stops recording... If you can find a camcorder which can be used as a webcam (i.e. outputs video continuously but without recording to its storage device) with the output going to a laptop with a decent hard drive, that would solve that, but
AFAIK few camcorders can work that way. Maybe the "showroom demo mode" might do it?
Hard drives tend to crash around FL130, IME.