Yes you could use a manual transmission gear box providing you could find one with a 3.33 to 1 ratio however the same reason applies for my suggesting using the heavier rear ends applies when running any gear system designed to run one way in the opposite rotation it was intended for you have to take into account for the input torque ratings which would be used as the output in this case which greatly reduces their rating hypoid gears of a diff are made to apply large amounts of torque in primarily one direction over long periods of time with intermittent use in reverse. the Helical cut gears of a transmission are designed for the same purpose. Also the thrust bearings are not designed for these extended reversed loads. To expect long service life from either a diff or a transmission in my opinion the original input torque rating should be de-rated by a factor of not less than 4 more if I were making it for myself.

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