Sony Walkman WM2

I'm attempting repair of a Sony Walkman WM-2 that has been in a drawer for many years. I've replaced the drive belt, freed the seized pinch roller and cleaned the capstan and pinch roller. Everything works but the tape wow is unacceptable.
I don't know what performance was possible originally but I'm sure this audible degree of wow would not have been OK.
Any ideas on what I can look at to fix the issue?
Many thanks

Ian
 
I think it is mechanical in nature, which suggests the tape spool takeup mechanism but I don't have a service manual (anyone know where I could download one?) and I'm not sure how much dismantling is required or how I would know if I'd identified a fault in that area.