Hello Jon,
Wait for a day to sail with a light steady wind, not too many gusts.
Sail the boat with the wind at 90 degrees to the left or the right.
When a gust hits the boat, watch which way the boat turns.
IF, the boat turns INTO the wind, the sails are too far rearward.
IF, the boat turns AWAY from the wind, the sails are too far forward.
To keep the mast in the same position as it is now, new sails should be fitted with the
Centre of the sail areas moved to correct the boat.
A Swing Rig sail setup, is designed for a particular boat, I don't think you will be able to get your boat to sail well with it.
Use the present mast position and make and fit some new sails, a small Jib and a large Mainsail.
As a starting point, find a picture of a boat that looks similar to yours, note how the sails look, do they look like yours?.
John.