Hi,
I've never flown SAA but I know that the stroller doesn't count as hand luggage. You can push him through in it and just before you board, you hand it over and they'll put it in the aircraft for you.
Sorry , I can't help with the car seat info. We've only flown once with the car seat and it was when our lg girl was 18 months. After that we never bothered to take it.
You'll see, he'll sprawl out quite nicely on his chair and onto yours - he'll be in 'first class'. I'm sure he'll sleep fine, our 2 always do. Its us who are like zombies.
If you really want his car seat and SAA have these rules, then pack all the things into one bag - it will be easier for you anyway- and let him take his car seat. If they give you any hassle, which I don't see why they should, tell them that you paid almost, if not full fare for the lo and ask to speak to management .
If you're renting a car, they also rent the car seats.
Yes, do the full leg compression stockings and try to move around.
Good luck and enjoy your holiday to the UK.