I can't advise much on how to split your nights seeing as I haven't been to all the parks you've mentioned but haing just come back from MZNP I can give a few tips there.
I'd try not to go when it's too cold. MZNP often gets snow and some of the loops and 4x4 tracks may be closed which would be a pity. The Sonnerust Loop is particularly enjoyable. The MZNP campsite is great, just be sure to mouse-proof everything! I had a four-striped field mouse make a nest in my hiking shoes, and ate through my sock just fro good measure! The shoes were inside our tent at the time!!
3 nights is plenty for MZNP, although they will be fairly full on. We did a night drive the first night, a short morning walk the next morning, and a cheetah walk on the third morning. Bear in mind that there aren't many species of game in MZNP and what is there is relatively plentiful, though some of the larger herbivores such as the buffalo can be tricky to find. Go to MZNP rather for the views and the amazing scenery!
Speaking to other campers who'd already been to Karoo/Camdeboo, they sound very similar to MZNP, although being newer parks, the landscape is still slowly reverting from farmland to bush and some areas are a bit degraded? But as I said I haven't been there so I can't comment directly.
Addo is lovely, but it can be VERY busy; especially over long weekends. We camped there about 2 years ago and the campsite was cramped and very noisy. Also when driving around the park, because of the nature of the bush (short and scrubby!) we saw far more vehicles than animals.
I'd avoid Addo over a long weekend or public holidays and try go another time when it's quieter.
Hope that my ramble helps! Enjoy the planning!!