My LO was a really difficult baby. Really bad colic for months, no naps. Was at my wits end until we forced him onto a routine. Relative calm for a while.
Then at ? (can't remember) months, biting, slapping, etc started. Used to frustrate me that we gave us no cuddles. Thought there was something wrong with him. Just a phase. Didn't last as long as yours though. I really stuck to his bedtime routine, stuck to the 'firm voice, no attention if he bit me' thing even though it felt like it was doing no good.
Eventually it stopped.
He is now a VERY boisterous three year old. Makes it worse that he is so tall for his age because if he decides to, he can really hurt other kids. On the other hand, he is VERY affectionate - loads of kisses and cuddles. I am now 39 weeks pregnant and he swings from kissing my tummy and whisperring to the baby to attempting to knee drop on my tummy, shouting, 'I squash the baby mummy.' What a monkey!
Does your LO go to nursery? If you are stay at home mum and you can afford it, it might be worth giving him some time at nursery.
Yes, he might hit other kids but all kids do that from time to time and the staff will know what to do. Don't get me wrong - I am NOT recommending that they do your job for you - it's just it will give you some time to yourself, it will give your LO some really great time with other kids.
I pick my LO up regularly and have to sign an equal amount of 'incident forms' (where he has bashed another kid) and 'accident forms' (where he has been bashed by another kid. He loves nursery - they do loads of fun stuff that I couldn't never be bothered (sorry!) to do at home - flour play - yuck - and also cool stuff that you can only do with ten other crazy three year olds.
It's really hard for you to take your LO to playgroups because you seem him bashing other kids with a 'mother's eye' whereas at nursery, they are used to it.
Sorry - one more thing. My only other advice (which is really hard) is to get outdoors as much as possible - wears them out and they can do less damage. Blanket, toys, field.