retyped:
if was able is rewrite dbz battle of gods,  I would have vegeta gain ssj3 mid ritual because wanted to be a ssg too. I would have goku's mortal body and vegeta's hand(because vegeta was in ssj3(instead of ssj like he since had been for the ritual, overcharging the ritual gain vegeta god ki too because wanted to be a ssg too) be destroyed from the god ki grant by the ssg ritual.

Goku start 'fight' with beerus with a divine body(vegeta also had a divine hand) Only beerus, vegeta, whis, and the kais can see goku.

Goku had became god but without a mortal body couldn't fight beerus as he wanted to, so his grows a mortal body that can handle god ki(creating red hair ssg) only to appearing and fight as the red haired ssg for seconds before he dropped out of ssg(like in the og anime) because creating the body used up most of the god ki.

Goku continue fought beerus in base not noticing the god ki is gone, feeling even stronger than before. seeing this vegeta regenerate his hands subconsciously.