Your suggestion for a pro quality video camera with great audio under $500?

I work at a trade school we we have weekly guest lectures, presentations, and other events, and we're wanting to take some quality videos to put on our site and elsewhere. Typical iphones and other similar devices are just giving us poor quality, especially audio, so we're looking for suggestions for a quality videocamera under $500, with the most important attribute being good audio pickup.

My definition of a "pro quality video camera":
Lens diameter 67mm or larger;
Imaging chip 3CCD or 3CMOs array 1/3" or larger or an APS-C sized single imaging chip (or larger);
XLR audio inputs.
When the video camera has these, all the other pro functions on the outside of the camera are also available and not buried in a menu. Manual focus, manual zoom, manual audio gain control, white balance, video gain, and more.

At under $500, you are in the higher end of the entry-level consumer grade camcorders. At best, with a 47mm-58mm lens diameter, single 1/3 inch imaging sensor and a single stereo 3.5mm audio input. Like a Canon HF R500. Limited manual controls. Be sure to include - and use - a tripod or other steadying device (don't shoot handheld, that screams "amateur"). Use external mics. In this case, with limited budget, an Audio Technica ATR-6550 shotgun mic and a Audio Technica PRO88 wireless lav. There's no single best mic. When the built-in mic is in the right place for the audio, the video framing won't look right. When the framing looks right, the mic is not in the right place. Decouple the mic by using an external.

The least expensive "pro quality video camera" that meets all of the attributes in my definition is the Sony NEX-EA50UH. It is about 4x more than your stated budget. It is an "entry level" pro-grade camcorder. Do not consider dSLRs unless you are willing to deal with overheating and auto shutdown, file length limitations and other known, published, issues (read the manual before you buy).

If your definition of "pro quality video camera" is different from mine, please let us know what that is.

And someone gets to learn to edit…