Most likely this is a semantics issue. "6 lead" technically means that there are six leads INSIDE OF THE PECKER HEAD, but you only bring 3 wires into it from the starter. On a Part Winding start configuration though, you bring 6 wires into it from the starter, but usually there are 9 or 12 "leads" inside of the pecker head. From the wire numbers, I'd say it is a 9 lead motor. Sometimes even if it is technically a 9 lead motor, you may only be able to see 6 of the 9 anyway, especially on older motors.
To make that work with a VFD supply where you are only going to bring 3 wires in from the VFD, you need to combine the two sets of windings. Look at this diagram:
For connecting a VFD, imagine that there are no contactors and each pair of wires must go to the VFD cables. So from this is looks as though you did it right, 1-7 to L1, 2-8 to L2, 3-9 to L3. But here is the caveat...
This diagram is the NEMA standard. Unfortunately not everyone uses the NEMA standard for Part Winding motors. In this drawing, 4, 5, and 6 are internally connected together to form the Wye (but as I said you may or may not be able to see them). I have seen some where 6, 7, and 8 are used instead of 7, 8 and 9, and the internal Wye ends of both sets of windings are all called "9" because they are all common to each other. Sometimes in that configuration, you will see 6 wires all with a number 9 on them, sometimes it is internal and you don't see them at all. We can't see your pecker head connection diagram. Does it look like this?
If this does look like your diagram, are you using a breaker that came from the old PW starter? Because if so, it might be too small to work for an Across-The-Line bypass. Technically, PW starters are supposed to have separate breakers (or fuses) for each set of windings, although that was a late change in the code and there are still a lot that do not. But if yours was one built to the newer standards and you are only using only one breaker, it may not be able to hold in under A-T-L inrush current.
As to the VFD faults, are you trying to use Vector Control? If so, did you perform an auto-tune? If not, VFD default settings for the motor parameters would not take into account the differences in the motor between standard and PW connections. Auto-tune would (should) have picked that up. If you are just running it n V/Hz mode, it should not have cared.
If those are separate windings, energizing BOTH at the same time would be interesting. If the 6 leads are the two ends of the three windings, that would be even more interesting.
