The story of hundreds of cars at Kruger worries me a bit.
It attracts a lot of day trippers at weekends, and obviously school holidays and public holidays are going to be busiest. Perhaps if you must go into these times go for the private reserves that are open to the park animals where numbers are controlled but this is much more expensive.
We were there in October and saw nothing of these crowds, but it did get busier at the weekend. We saw all of the big five except Leopard, which we missed by a gnat's. Our driver saw the tail disappear into a bush and we couldn't find it again. We saw a fresh cheetah kill where the cheetah called to the others and we watched 5 of them share the kill. We saw a Lion stalk and kill its prey then eat it, only a few yards from the truck. It was only a tortoise but it made some interesting crunching noises! Had some very interesting close encounters with bull elephants in must.
However for me it is taking your time and looking at all the smaller animals that makes it so worthwhile. Tortoise, snakes, chamelion, birds, small mammals, birds, loads of interest there. The walking safaris are, of course, limited numbers and to be thoroughly recommended.
Book your accommodation in the parks early, especially where you go over a weekend, we stayed only in National park accommodation which was cheap and to a high standard.
we weren't self drive but had our own guide with just the two of us in the open 4x4. Some companies work on only small numbers in the vehicle which maximises photo ops, but we were lucky just to have the two of us. Our dates didn't coincide with anybody else so we were alone. Self drive obviously achieves the same, though with closed vehicles and no local knowledge or radio support. (the guides talk to each other so they can find the animals, but they do it in code so that it doesn't get widely broadcast.)
Our guide picked us up from the airport in Johannesburg and drove us to Kruger in a minibus, where we stayed the night outside the park and swapped to the open 4x4 in the morning. We then had a week in Kruger before he drove us back via the scenic route stopping in the mountains and at Bourke's Luck before returning to Johannesburg.