I seem to remember that when we had a very old Ransomes Auto Certes into the workshop we used to pray that the recoil was working because the older models were fitted with the BSA sloper and the recoils weren’t compatible with the later Villiers produced engines. We couldn’t get parts for the BSA recoil at the time, and this was back in the 1980’s
How they were different I cannot recall, but once BSA sold the design to Villiers there was definitely a change of recoil starter (probably to fit in with existing Villiers designs).
Your only resort may be to change the cowlings to the later sort.