My 1973 Nauticat 33 suffers from the same problem, main reason being the small size of the skeg mounted rudder . I do not think that a larger genoa will help because the sheets enter the hull behind it’s turning point.
Unless there is a brisk wind abaft the beam to give the boat sufficient speed through the water for the rudder to be effective I do not hoist the mizzen. If the wind is before the beam and tacking is necessary I have to have the engine ready to help her round.
Also, unless the wind is sufficiently aft to enable goosewinging, I find it better to not hoist the Main when running before the wind because it shades the genoa which has much greater pulling power.
I may be missing something here.