SS will fluctuate - because of the resistance increasing when heated it can be used as a TC wire, but because the increase in resistance is minimal it is best not to go much below 0.30ish ohms in TC mode, preferably a bit higher to give the chipset a fighting chance of accurately reading the resistance increase because it isn't much.
Because the increase in resistance is minimal, particularly with low ohm DL builds, it can be used for Wattage mode. In wattage mode it doesn't really matter if the coil resistance is slightly higher when it is warm as a regulated mod should adjust the voltage it sends to the 510 each time you press the fire button based on the resistance it reads at the time, even if the resistance is locked in there shouldn't be a huge variation, maybe a couple of watts max.
If you're having to vary the power between 5 to 12W I doubt it is the wire that is the cause of the problem - it sounds like a bad connection to me as the only time I've had similar problems it was down to a loose/bad connection in the atomiser, With pod systems I always suspect a loose connection because of most of them relying on a couple of small magnets which are never going to give the same contact pressure as a threaded connection and the slightest free play in the pod could disturb the connection creating temporary higher resistance, the mod then sends higher voltage and you end up with a vape that is as hot as fck - thats probably why you're having to drop the Wattage to 5 Watts..
If the grubscrews are gripping the wire firmly and the top of the mod is clean and dry, maybe trying a different pod if you have one to see if the different magnets give a better connection.