I sail a ketch....
My 'new to me ' boat is a ketch and recently sailed it across the Gulf from Florida to Tx. I never sailed a ketch before, so this happened to me also. All i did was let the Mizzen out just a little and that cured the problem. Just think of the mizzen as a 'tail feather' or weather vane. This usually only happened when in 20 plus winds and close hauled.At one point, when someone else was at the wheel, they couldnt seem to fall off and we had a small oil and gas platform right in our path.Boat would not respond and we were dead on target. I let the mizzen out and we regained steering.Before you think about making a cutter or more properly a 'double headstayed rig', you ought to go onto a more boat specific site and see if they were ever manufactured with a double headstay. Then you will be able to talk to others that have that arrangement and get the dimentions and specifics.Good Luck.