Most of us are quite happy gybing with normal size wings (but perhaps a bigger wing is more comfortable for those who prefer to do things slowly)..
There are two completely separate moves needed here, the footswitch and the gybe. I strongly recommend you try to master the foiling footswitch and only after that continue into your gybe which is the easy part.
Maintain good speed and get comfortable while keeping your kite quite high at 11 or 1 oclock. if you use straps take your back foot out of the back strap and put it just in front of the back strap. Rotate you stance so your shoulders are in the position they will be in after your footswitch. Now while KEEPING YOUR UPPER BODY AND SHOULDERS ABSOLUTELY STILL move your back foot to the front of the board (into the front strap if you use straps). That's it.. you are almost done.. you don't even need to think about your old front foot because you will naturally want to move it to the back of the board to keep your balance. The key is to have your upper body in position before you move your feet!
One other tip: do NOT look down, keep your eyes on the horizon.
After this footswitch you will find yourself riding toeside. Enjoy it for a while and then whenever you are ready turn downwind, downloop the kite (to give you a surge of power), and then continue carving around to heelside. This is the easy part.