I was wondering what the gear of choice for this event would be.
re inflation: those small gas cartridges, electric pump or something else
re positioning: do you try to get 1 in every few people along on a ride to bring a stand the bash plate can rest on or wing it somehow with the sidestand?
How many spare tubes to people typically take on a ride?
You should always assume that you are alone out there, in saying that you need to ensure "YOU" are prepared. If the group is really a tandem you need to prepared in the event you need to go for help should the need arise. In a larger group, perhaps all the essentials will be available or maybe not. Flats aside, you need a basic survival kit for small groups. For tire repair, build yourself a mountable kit, with irons, patches and a bicycle pump. Other pumps are easier, provided nothing else failed. The "Law of Averages" comes to mind.
Gas cartridges have limited capacity, when they are exhausted, so are you. Electric pumps, well anything electrical and mechanical can be prove to be unreliable. Bicycle pumps as used for mountain-biking is an extra safeguard. Take two!
As for getting the wheel off the ground, be inventive. The materials required are all out there. If you are pissed at your steed and it is already lying in the disk side up position, you can fix your flat as it lay. Just a thought.
One tube is required, the front tube will work for both repairs in a pinch. If you use it in the rear, replace it at home.
If you are in a conundrum, as a last resort you can fill your tire up with grass, twigs, bark mulch, almost anything for that matter, to get yourself to safety. But without tire irons at a minimum, profane verse will be the order of the day.