RAGB is known as a right angle gear box, housing two gears and changes the power output from parallel to perpendicular making it easier to run a chain to your axles
a shift on the fly trans isnt that common anymore, hydrostatic has taken the lead on transmissions. normally a trans like mine isnt on the fly, but can be coerced into shifting while in motion as long as you dont SLAM gears.
all tractor transmissions have a differential, "all" being the ones that wheels are connected to them directly, not by chain or other means
your idea will work, but finding RAGBs and welding the diff are your BIGGEST setbacks