Start from the beginning again.
It came from a lab, so presumably worked ok connected to a 400V 3ph supply. Therefore it should also work ok when connected to a simulated 3ph supply from a rotary converter.
The tricky questions. The rotary converter outputs 400V 3ph?. What size is the motor in the rotary converter? If you are trying to start 7hp then it really needs to be pretty close to 7hp.
Ah, those awful contactors! Just scrapped an A&S with those in, updating them to modern contactors is a really good idea, BUT, make sure you have an ACCURATE circuit diagram first.
Testing a rotary, or static, converter is simple, al you need is three analogue voltmeters that will read to 500V AC. Connect the VM across the three phases, start lathe whilst watching the voltmeters. One phase will stay pretty close to 400V, one phase will dip, one phase will rise. It is the amount of dip and rise that is important. Using the 400V meter as a base, the dip and rise from that reading should be similar, within 20V or so. Now try the high speed and observe the meters. My guess is that the 400 will be similar but the dip and rise will be very much larger, 100V or more. This means that the capacitor phase splitter in the converter isn't large enough.
If you want three Avo8 meters they are here for the taking, just off to the scrappy. I have three of the equivalent GEC Selectest meters, no real difference other than they don't explode if you drop them.
Last comment, don't even think about fitting a VFD. The static/rotary converter will quite happily run this sort of machine.