The schematic - yup, though I'd be interested in the 1c1/1c2 arrangement - these are contactors?, what actuates these? a mechanical forward/stop/reverse switch? in which case this can be re-used - which is what I think you're after?

The other thing is to look to see if you can only energise the start coil whilst the run coil is energised - again, can be done with the 1c1/1c2 arrangement, depending on it's behaviour.