By looking at the out drive, the slot is too deep there not a lot of metal there to hold under the stress of power or the drive shaft is too deep in the out drive under compression and the drive shaft wedged in the out drive and broke it. I would grind off or machine off some off the outdrive. Or take all the axle shim out of the inside of the hubs to move the drive shaft out closer to the end.
Do u have a pic of the buggy put together , close up of the out drives.