what weight aim do you have?
I would suggest that it’s likely the PAP machine already has regulation in it, and possibly may not have an issue with over 12.0v. You should measure the output voltage of the pack you’re using, over time, to see how the tolerance of it’s output is, as that may show you if it’s possible to just use the packs of multiple 3.7v’s without regulating.
Doing some reverse engineering of discharge rates and expected runtimes on one of the other batteries on the site you listed above ( [url]http://www.cpapbatteries.com.au/webpages/Fisher-Paykel-CPAP-Battery.html[/url] in particular) shows .65A discharge rate of a 10.4Ah battery giving 16h (using the @ 6CM rate). That means the “222 W” battery is a 12v 15.6Ah battery. Do you have an indication of the current draw of your actual CPAP units? Looking at the stats of the 222 unit, what approx hours of running time equivalent do you get, and what CM rate equivalent is that? It obviously changes the discharge rate and may have other implications for your batteries
If you didn’t have those batteries sitting around, I’d have suggested a LiFePO4 battery pack. Even small packs are quite energy dense, take for example the ~1kg pack from [url]http://www.gebattery.com.cn/product/12V_Car_stating_battery.html[/url] is a 6.4Ah, or an 18Ah battery is ~3kg.
So back to your questions.
1] What else would I need to be concerned with and
2] How many 3.7v 2200mah cells would I need in this sort of setup, to reach the same level of 12v power-bank-ness as the cp222 I listed linked to above? (I’m sure there is a simple formula)
2] first.
each 4x cell pack is nominally (3.7x4)=14.8V, and hold nominally 2200mAh or 2.2Ah. Then, you add the 2.2Ah together each additional pack you add. To get to the same ballpark of capacity as the 15.6 calccuatee above, you need to have 7x sets. An eigth pack and you’re nominally over their rated capacity. But, I suspect you wont be able to get the same runtime out of those; typical Li-ion batteries (assumed based on your 3.7v) don’t have anywhere near the rated capacity, maybe it’s 1.5Ah not 2.2Ah per 4-pack. The best bet would be to experiment and see.
1]. INSULATION. You have 7x packs, 14x wire junctions as a minimum, and a reasonably high discharge capacity battery, insulation is one of the biggest concerns. Insulate between packs as well. Don’t skimp, you don’t want to burn down the tent!
The standard wires will probably not be rated to .65A, you may need an upgrade (I’d suggest some high quality automotive wire with good insulation). Remember that you’ll heat the wires a bit, hence the reason for good insulation there too.
Charging will be a right pain. You have to charge ~30-odd batteries at a time. Just tracking which ones are charged and which aren’t is a fun task :). But if you charge all 100 and take them all, you get 3x the duration before needing to worry, so that’s a positive, right?
Single failed cells will screw you over. Make sure you check voltages once you discharge them and check they’re all within spec, and repeat after charge.
Structural integrity of the “unit” also becomes a factor since you don’t want to have to diagnose broken / loose wires at the campsite.
I’d spend the weekend testing a 7xpack out to see what runtime you get. At home, where you have a backup power source 
) its under 1A. 3x is crazy.