First, since you've never used a carto in a carto tank, I'll offer this. While it is certainly possible to fill a carto-equipped carto tank without a tank tool, such a tool as the IBTanked drip tip/tank tool or Slap Yo Mama tank tool, makes it easier. Most carto tank users probably use a tool and they can be used in the Sophia.
I have successfully used one of my tightly fitting, single o-ring drip tips to turn the juice flow control in the Sophia. Because that particular drip tip's diameter is smaller than a carto diameter, I can push that drip tip down into the tank and remove the Sophia base to work on the wick, etc. HOWEVER, because this drip tip doesn't seal at the top end cap, it is imperative I find a way to keep the tank vertical and not falling over, else liquid would pour out. A tank tool can push the Sophia down (as when filling), but the tank must remain vertical in that condition. With a straight drip tip of at least 10 mm length, such as By Leo's STR10, STR15, or STR20, or others like it, both ends of the tank are sealed and the tank can be laying on its side while the base is removed.
Another option is the ByLeo "Nail" drip tip. Pushed in some, it leaves a gap for filling the tank like a tank tool. Pushed further in, there's enough of a straight section to seal the tank while the base is out of the bottom.
I hope this helps.
EDIT TO EMPHASIZE: This is only an issue with a 45 mm carto tank. With the 45 mm Sophia in a 35 mm tank, a straight drip tip is not needed to seal the tank.
EDIT TO RESPOND TO YOUR EDIT: I don't know of any carto tanks that come with a screw on mouthpiece. A carto tank slips over a punched or slotted carto. A carto uses a slip in 510 drip tip.