I would advice against placing Gizmo back in his cage as form of punishment for biting.
1. He is already resistant to going back to his cage, hence the biting when it's time to be put back in cage.
2. If placement in cage becomes regular punishment for misbehavior, he further learns that cage = punishment, which will only make him want to avoid it even more. This can lead to more biting, and screeching/screaming once he's placed in his cage (even if he's not being punishment, but being placed there to go to bed, etc).
Instead, reinforce him for going back to his cage. Give him a treat once you're able to put him back in. Verbal reinforcement works wonders, too (i.e., "Good boy, you are such a good boy, Gizmo!"). And of course, he's more likely to enjoy being in his cage if it has plenty of room with plenty of toys and treats. Basically, you want to reinforce your bird as much as possible for being in his cage. This will help him associate his cage as a more happy place to be, making him less resistant to go back there.
As far as what to do to when he's biting - - whisper to him. Whispering can be very distracting, and parrots will usually stop whatever it is they are doing to listen. If Guavo becomes nippy, I'll usually look him right in the eye and whisper, "Guavo, we don't bite." If need be, instead of placing him back in his cage - - place him down on the floor for a few minutes. It's better he learns to associate being placed on the floor as punishment, as opposed to being placed back in his cage.
Most importantly, learn to read his body language. Biting is usually a bird's last resort of telling you to back off. When youv'e failed to read his body language (i.e., proceeded to pick him up or pet him when he'd rather be left alone) he will bite. So respect your bird and his choice in the matter, and he will be less likely to bite.