OK, so was the shift handle loose on the shift shaft, seems like you confirmed that it was. This is all it takes to cause shifting difficulties. Clean up the threads on the screws and tap out the hole on the shift handle to ensure the shift handle can be secured properly to the shift shaft. This slight adjustment is there to align the shift rod and shift handle vertical detent. This adjustment is there to help center the adjustment to ensure you have good forward gear adjustment and the unit is actually in neutral when the shift handle is in the neutral detent..
Once this adjustment is made, and you are sure there is not slop in the shift rod/linkage, you can water test again. I’m just hoping no internal damage has been caused the the sloppy shift linkage.
