I am certain that you do not need to be as academic to get into the indies you mention, than the super-selective South/SW London grammars.
However entry is less predictable. Indies will tend to look more at potential contribution, either academic or music, sports, art, drama etc. They also interview which grammars wont and seek references, so can pick up interesting children and perhaps weed out ones who might be more trouble than they are worth.
Alleyns and Whitgift in particular tend to be less predictable than, say, Dulwich College. The latter has a far larger intake and so as long as your son is comfortably within the academic range, and it sounds like he would be, he should be OK. Alleyns is mixed (so half the places go to girls), has a prep and gives a certain amount of priority to siblings, and so there simply are not as many places available for boys. It has a reputation for looking for children who will fit well into their school, and having a second string like art, drama or sport probably helps. Whitgift appears to have risen in popularity over the past few years and again the issue is more one of outshining the competition than achievement levels as such.
Unless you really feel that it would cause real problems for your son, the best approach is to have a go and see how he does. Not getting a place in either of these schools does not mean a child is not good enough. Simply that a lot of good kids tried and they could not all be given places. You have the back up of a good state place. Lots of kids will be sitting for up to five, and perhaps even more, indies. The competition is such that few can be completely confident that any one school will offer a place.
Preparation should be around the specific papers, not around SATs.