My wife and I have gotten into a bad habit with our 3-year-old. When he misbehaves, sometimes he bites or otherwise physically assaults one of us in frustration, particularly when we are telling him he cannot do something he wants to do. We will then tell him he shouldn't bite, that it hurts, and then he'll laugh at us and act as if it's a hilarious game.
These aren't little bites or hits, mind you; they're very painful, and they often make the recipient quite stressed out. Further stressful of course is the laughing and gamboling about. This usually happens when he's a bit tired (and thus hyper). We will then make some effort to take him to a time out, but it won't work; it will devolve to that parent having to physically restrain him to keep him from running around and ignoring us, which just leads to another biting or hitting incident, and the cycle repeats.
We're well aware that essentially none of this works, but we haven't been able to come up with something that does, and is reasonably doable during these times. Our son is pretty mature and able to be talked to when he's not over tired, and normally behaves quite well; our discipline usually only has to be occasional time outs, and the worst thing he does on a normal day is complain too much that his screen time is over. But when these incidents occur - probably 2 times a week - it's a completely different story. Once we do get him calmed down - often after getting him to go elsewhere - he's able to understand that he shouldn't lash out in frustration and talk about it, but getting to that point is what we can't seem to do in a calm manner.
We've discussed all sorts of options, and don't really like any of them. We don't like having nonimmediate penalties (i. e., removing privileges), as he's just barely three - from what we've read (and seen) he isn't old enough to understand them. We're considering star charts, but we don't have a lot of confidence there; the core of the issue is that he gets tired, either because he misses his nap (which he does fairly often, as he's not a good napper) or just because it's 7 or 8 pm.
What should we consider to deal with these outbursts? What works well with otherwise well behaved children who have lost control over their behavior?