DIY Rotary Phase Converter with starter motor, cutout relay in parallel with load?
The RLY1 needs to be delayed until the start or "pony" motor has brought the idler motor up to speed. Delaying the energization of the start motor until the idler is up to speed is what avoids the "monstrous" inrush current. There will be no voltage on L3 until RLY1 is energized, so RLY2 may not de-energize the start motor soon enough. You will need to either use a manual starting sequence as shown in the paragon code link or use a time delay relay.

Probably something like this: