It is amazing to me how you guys punish yourselves. You are trying to learn a little about the subject and you do something like this to yourself.
Instead of scratching your head with this, why not get any old three phase motor that you know runs on 240 three phase and put it to work.
It needs to be a little bigger in HP than the biggest HP motor you want to start.
It will be your
IDLER
It has three legs. You put 240 single phase (which has two hots) to two of them.
You have a switch or circuit breaker to do that
You start it someway - it will not start itself. Spinning it up with a rope before hitting it with the power works. There are of course fancier ways to start it, but don't confuse yourself just now
When it is running, the three legs are all hot. You feed this three hots to the machine three phase motors with safety switches/disconnects so it is safe.
They like it and start right up. The home made three phase isn't balanced yet, but that can come later. The silly three phase motors won't seem to care. They will just run. If you start the idler backwards, everything in the shop will run backwards - so pick a direction to spin it and keep to that direction.
Plenty of help here if you ask questions that can be answered.
John Oder