Well, mine doesn't have washers so I can't help much there but as for the wiper controller It is possible that the one you bought is not Corvette or not '58-'62. Chevy called it a controller since it is not electrical. The same part, # 3743413, was used in all '58-'62 Corvettes. Prior Corvettes and other Chevrolets used a different number. As well as I can remember from my old GM parts days the only difference in these parts was the cable length required for the specific application.
The one you bought could be for a '57 or older Corvette where the controller was mounted in the lower middle of the dash and required a shorter cable. Or it could be for some other Chevy.
Bottom line: If it hasn't been altered and the cable is too short it isn't a 3743413. I'm not sure if the cable can be replaced. Seems like some sources used to rebuild these. Anyone else know?
Tom