As James rightly says, there was a lot of space in a Sunderland for additional fuel tanks or whatever else was needed to be carried.

The only reason for strapping something on the outside of a Sunderland (mini subs/Chariots etc) was because you needed to drop them off at some point, and they wouldn’t go through the door.

The reason the Sunderland didn’t carry more fuel was the power needed to to get it off the water in a suitable short distance and, once more powerful engines were available, the spray from an overloaded aircraft causing damage to the propellors. The hull pounding on the water was less of a concern, surprisingly.

There was a constant battle between adding more kit to the aircraft (radar etc) and the need for fuel to get long range over the Atlantic.