As above, you can be driving an unregistered car for only one of two reasons.
1 - To an inspection station in order to get it registered, or
2 - To a place where repairs are to be made so as to prepare for the inspection.
Problem is you were driving to your house. Dont think this is allowed.
And to be honest, I dont really believe the story 100%, and I doubt the cops will.
If you can genuinely say youre telling the truth, its a shame and I feel sorry for you, but I dont see you getting out of it.
If not, well you shouldnt have been stupid enough to drive an unregistered, uninsured car.