Hi Martin,
I hope you won't take this amiss but you remind me of a very good friend of mine. He's a smart cookie, very good at most of what he does and very confident. He has a blind spot though; he thinks he's good at everything, and no-one is that! Once in a while he comes a cropper and can't believe he got it wrong.
Electric motors are not simple and they are not all alike. I find them very confusing. Reading back through the thread I see a couple of places where you asked for help and then missed requests from experts like John and Les asking for more information. What they were trying to do was establish what type of motor you have and what the various connections are for. I can't see where you answered their questions, which is why Les suggests you've been guessing.
Later you published a series of wiring diagrams: I didn't realise these were asking for help, rather I thought you were telling us that you had got the answer! You seemed to be making good progress,
Francis (who knows a bit!) advised against reusing the old motor wiring. He's absolutely right. Once a motor has cooked all the insulation is compromised. He's trying to help – he doesn't want you spend a lot of effort repairing a motor that's likely to fail again.
Others have tried to explain that rewinding a motor by hand is seriously difficult to do. It will take forever, and it may not work when you've finished, even if the insulation is OK. It's akin to me (a very inexperienced Model Engineer), saying I'm going to start by free-lancing a 2-10-2 locomotive in 9" gauge and is it OK to soft-solder a boiler made out of Titanium.
If I were you I'd start again. Buy a new motor with a data sheet. I'd try with a VFD and 3-phase, they do work despite your first bad experience. Once bought I'd come back on the forum and start a new thread asking what to do. John, Les and others have successfully helped many others with lathe motor problems. The secret is for you to carefully answer their questions and patiently take their advice so that they can guide you through the maze.
I was going to advise you not to get discouraged. Looking back I don't think you need that. Your adventures with electrics may not have gone well but no-one can criticise your determination whilst the photos show you've done a fine job on the mechanical side.
Cheers,
Dave