Ken -
Not sure if this will work with your motor and switch ... but here's a schematic I came up with to run/reverse a 220 volt motor with a Dayton drum switch and just 4 wires. The schematic includes a picture of the drum switch contacts and what goes to where for forward/neutral/reverse ... so you might be able to cross reference it to your switch. The schematic also shows what wire goes to what winding, etc. inside the motor.
This was for my vintage Grizzly 12x24 lathe. The original switch was shot when I bought the lathe. I'd previously wired it up to the drum switch with a 6 conductor cable, but that scheme always left one motor coil connected (unswitched) to one leg of the 220. So I came up with this "improved" schematic. Didn't actually wire it up, because I went to a 3 phase motor and VFD instead.
Hope it helps!
- John