I'm not sure that assumption is correct.
I think that the underwater lateral area is the area seen 'from the side' - i.e. the lateral projection of the hull.

You might very well be right. I wasn't sure of the meaning of the word "Lateral". That means that method 1 and 2 is actually the same. The only difference is that method 1 uses 3,33% of the lateral area.
If I recalculate method 2 the result is between 58.08 and 116.16 cm2. That seem a bit too small compared to the rudders you mention.

The problem this formula is that it doesn’t take the width of the boat into account. And a kayak is narrower than an average boat.
I am not sure, but I assume that a narrow boat is harder to turn than a wide boat of the same length. And will therefore require a larger rudder.
Imagine a round "boat" like a swimming ring or a life raft. They will turn very easily (But not move very fast)

For reference, the underwater part of the SmartTrack Race rudder on my Thomasson Panthera is 8cm x 20 cm; on my Think EZE surfski it's 13cm x 20 cm

Palle