uff snails for 40 amp for each one I think it won't give you space for the 3 separate coils. I tell you it is because I made a battery charger with a microwave tx I placed 75/90 ° thwn # 10 cable that according to table supports 40 amp and to get the 14.5 V after the rectifier bridge that manufactures it too. I had to give that cable # 10 the amount of 9 laps and the remaining space is very little. I will take pictures to see if you notice but I do not see the option to send the photo you take.
If you make three coils giving each one of 9 to 10 turns to reach 12V, try to use wire that occupies less space and not cable as I use. Another thing I did 9 laps but my primary voltage here in my country is 110 vac I don't know in your locality.
To handle the amperage in question, my brother who works by winding uses # 15 wire for alternators. As for the diagram let me and I ask to be sure.