Ohm tells me that for 220w @ 0.23 ohm you're pulling just over 30 amps @ ~7v.
Your battery is rated for 20 amps continuous discharge.
Even @ 150w, which is the highest I would bother with for a 2x18650 mod, you'd still be over 25 amps. Since Wattage is just vols*amps, if you can increase the resistance you can push more wattage without increasing the draw.
You can get batteries rated to 30a or 40a continuous discharge, but I can't tell you if you're mod would take advantage of them. It may assume ~20a as a max.
Though your mod *should* prevent you from overdrawing the batteries, I wouldn't suggest tempting fate by running that high regularly. Even with regulated mods it's a good idea to stay within relatively safe parameters.
I can't say for certain, but I suspect what is going on is that your mod is pulsing (or lowering the wattage and not informing you), and that your 220w is effectively much lower. If it's pulsing, you may not find that perfect spot, as it's really a combination of powers (though you may be able to come close). If it's just lowering the wattage to a fixed value, you should be able to find that value, may just take some trial and error if you don't know how the algorithm to limit is designed.
Keep in mind I'm not experienced with your mod, so what I'm saying above is general info, it errs on the side of caution and should be good for any mod really.