OK, those details (and especially the video) are very helpful.
So, if they are only using the one mic for the soloist, I would record them them as though they are a regular choir that doesn't use any PA. You will get the proper soloist vs. ensemble balance just by proximity. The best way would be up on a high stand behind the typical conductor position, but because of the low ceiling and the desire to do a video, I would modify that.
I have had good results in these restricted situations with a pair of cardioids in ORTF, DIN, or NOS array (depending on distance and width) mounted to a low stand right in front of the stage, and angled up so that the mics are aimed at the singers in the rear. If the room is really dead sounding, I would go with NOS as it will get you a bit less of the room than ORTF (although where you would be setup would minimize the room sound to some extent anyway). You do not want to use omnis in this situation - your AT's are the way to go.
Hopefully the soloist remains centered, as you do not want either mic pointing directly at him / her. This is how you will maintain the right balance. You also should be close enough so that the PA speakers are out into the house area past your setup. It's OK that your rig will capture some of the PA, but your typical "point-at-stacks" taper setup out in the house would be a poor choice here unless each member of the group is mic'd and there is a competent FOH engineer balancing them. For what you are doing, you need to control the balance.
I'll see if I can find some old recordings of a concert I recorded this way to give you an idea what it sounds like. Good luck!