Welcome to both of you!
It is not a busy day on this forum, so I'll take a whack at an answer so you'll have one. I'm going to come from a non-technical direction that is more about people than camera specifications.
Nobody anywhere is likely to own all three of your choices. So, your not going to get much technical review based on the way you asked the question.
You say you are buying for a school and will be sharing with other staff members. When you are buying for other people, with other peoples money, you should consider buying "mainstream" and "brand name" quality. Stuff happens and you don't want to be defending any unusual choices.
Canon and Panasonic are more in line for as front row mainstream brands than JVC. Canon is one of the two kings for DSLRs, not consumer video cameras. Of the three, my view is Panasonic is the leader of the three for consumer camcorders.
The mainstream video format standard, related to the wide adoption of Blu-Ray and the current crop of TVs, is AVCHD 2.0 that includes 1080p60 as a setting choice. Canon weaves around their description of HD, tries to make it sound like AVCHD but does not fully buy into the AVCHD standard.
So, if I have anything to do with it, you will buy the Panasonic HC-X920. It is the most mainstream, high quality, easy to use consumer priced camcorder on your list.
Will it do the job for a school?
- Multiple users? Yes, it has a terrific full automatic ("iA") mode that anybody can get good video with.
- Multiple formats? It has full AVCHD. It also has "iFrame" a MP4 variation for Apple iMovie addicts.
- Concerts and Plays? Those are not "low light". They are well lit so people in the audience can see. All three of these and most any other current camera or camcorder will record school stage events without any difficulty.
- Sound quality? There is none in a boxy room built for basketball. The X-920 will record the sound present in the room in 5.1 Dolby. If the school does have a sound system that can be (skillfully) tapped into, there is a mic input and headphones output for quality checks during recording. (Gymnasium sound will be your biggest problem.)
- Full manual control? Any of the amateur staff members that try to fiddle with that on an occasional use basis will make the resulting video worse, not better. Full manual control is for do it every day professionals and gear heads, not education professionals that should concentrate on the students. You want this to be easier to use than a teacher's iphone and with better results. The X-920 has enough manual control to handle truly unusual video situations or entertain you if you want to be a gear head once in awhile.
- Narrow depth of field? It is a wonderful thing for art films and photos. Getting it right in school concerts it is not such a good thing. You won't get a lot of it (under the laws of light, optics and physics) until you get a camera with a big diameter lens like an expensive pro camcorder or an awkward (for video) DSLR. The X-920 will allow you to manually open the lens as far as it will go and adjust shutter speed automatically to get the exposure right.
- Transcoding? That has nothing to do with the camera, it is about the editing software. Skilled videographers would much rather add quality to their video with grading, trimming, transitions and effects than limit themselves to clips glued together without a little manipulation. AFAIK, you will have to buy a PC that will run HDWriter (that comes with the x920) or "TMPGEnc MPEG Smart Renderer 4". Neither runs on a Mac.
- Long concerts and plays? Most video that people can watch without getting bored to death are under 10 minutes. If you really are going to produce full length concerts and plays on video, you need a BIG battery or be able to plug in to 120 wall sockets. If the x920 is the same as the earlier model I own, it comes with a power cord that can be used in place of the batter. The limit is then only the memory card that can now be so big you could get between 5 and 27 hours of video.