Before you assign the number of nights at each, you really ought to look at what you are going there for.
For instance, the big draws at Korcula include:
How much time do you need for that with some style and relaxation … or what ever your travel style is? I would give it not less than three nights if on the first day I arrived early.
Then repeat with the other destinations. Then if you end up in the same fix that I do, I find out I am short on time and start to have to make value decisions. One place I would study closely would be Bol. I have never been, but it does appear to provide a lot of potential for the sort of holiday that I enjoy. There is a winery or two and boat and fishing charters. That might mean more days for me than for you. Then Dubrovnik would be last and that might be good as it will be later in September and there will maybe be a few less cruise ships in the port.
But only after looking at the possibilities in each stop do I have an idea of how many nights. And my count doesn’t necessarily line up with anyone else’s because I am particular in what I enjoy and don’t enjoy.
When? Again, only you can be an expert. Anyone interested in Beach time? Or boating time? You always play the odds for good weather for outside things but outside is what the Balkans excel at … well for my taste.
Split Rain: September 1–10: ~17% to 19% chance of precipitation (generally clear, sunny, and dry with occasional light passing showers). September 11–20: ~19% to 22% chance of precipitation September 21–30: ~22% to 25% chance of precipitation (higher likelihood of occasional afternoon storms or passing rain systems, totaling around 66–82 mm across the latter half of the month).
Split Temperatures: September 1 average high 84 and low 65F which is beach and boating weather. September 30 average high 75 and low 59F which is not great beach and boat weather.
Tourism Load: I read a bunch of data but trying to distil it is near impossible. Split and Dubrovnik and Korcula are what they are; and my attitude is just to deal with it.
There is a reason that all those tourists come in warmer weather … why should I deny myself the same enjoyment. And I like nature when I can actively participate in it. For me that means boating, maybe fishing, swimming, walking and sitting outside with a beer in the sun. So, for my taste and for my enjoyment I would arrive in Croatia no later than the 11th of September if my departure date was the 21st. Doesn’t mean I am right, just means that those dates might give me the odds that I would want for the greatest amount of enjoyment for my taste while giving me some break from the overtourism that plagues Croatia.
Sorry, not much help.