I suspect your original motor might have had problems for one of two reasons:
1. Centifrugal switch which removes the start winding from circuit might have (intermittently) stuck. This would not be picked up during a rewind.
2. Lack of cooling due to sawdust build-up in the windings and or fan housing.
In your position I would look for a new motor and find a local metalworking guy to make an adaptor if a standard motor won't fit directly.
https://inverterdrive.com/group/Single-Phase-Motors/TEC-Single-Phase-Motor-1-1kW-1410RPM-4P-90F-B14/Where are you in the country?
Scotland, nr Stirling