wrote...

But remember the keel/fin/centerboard are symmetrical in shape so you get
equal lift on both tacks. So the keel's lift is negated.

Not so.

Just as with an airplane with a symmetric wing section (many aerobatic planes,
including the Pitts Special) generates lift when the angle of attack is 0, so
does a symmetric keel. It does so by sideslipping a bit through the water,
imparting a relative angle of attack. Same with the rudder.