Ok, I finally got home and looked at my service manual (bought from Binder Books).
I donâ€™t know what I was thinking when I said conventional design manual transmissionâ€¦Well actually I was thinking about a three speed rear wheel drive automotive transmission.
First I want to get the transmission terminology correct. The main shaft (upper shaft) of the Cub transmission is the spline and clutch shaft and the countershaft is the lower shaft.
In my picture the gears marked in yellow when meshed together would be third gear. The two gears marked in blue (second from right) when meshed together would be second gear. The two gears marked in orange (third from right) would be first and the two in red would be reverse. As you can see the main shaft first gear is used for first and reverse.
I know straight cut gears make more noise than helical gears, but the complaint (If I remember) was a rattling/grinding noise in second and third. Since second and third gear is one piece I would diagnosis the splines on the gear to main shaft are worn causing the gear to wobble (rattle) on the main shaft when in second and third gear. If I disassembled this transmission I would also check the main shaft (Spline and Clutch shaft) for wear, where the gear slides on the main shaft and check main shaft to countershaft gear (face) for wear. This would be evident by scatches, abnormal marks where both gears mesh together.
My thinking is, since this tractor spent its life in Florida, it cut a lot of grass most likely in second gear.