In my Gravely, I used 10w-30 dino oil in the transmission and 15w-50 synthetic in the engine. The 15w-50 Mobil 1 is exactly what I used. After about the 3rd change, it stopped using oil. I might have been able to go with a lower vis oil then, but up to that 3rd oil change with synthetic, it was still using and smoking blue on startup. About that time, I got my JD 4010 and sold the Gravely.
It would be better to use 5w-30 dino oil if you can find any, the lower the first number the less gear resistance in cold weather. I'd be leary of using synthetic oil. It's probably too slick for the synchros, etc. to work properly in the transmission. Mobil 1 offers a 0w-30 now, for instance, but you can't get a dino oil like this.
Changing the transmission oil, stopped my left axle seal leak almost entirely. I disturbed it (I guess) when I put the wheel brakes on it and started it leaking. The oil change almost stopped it (e.g. reswelled the seals).
Ralph