School admissions/Arrival in June (Nairobi)

Hi, my family are I are making the move from Baltimore USA to Nairobi around June, based on a job offer I just received. We are starting to investigate schools for our 6-year-old son, and I think we are narrowing it down to a short list of usual suspects--International, Hillcrest, Braeburn, Peponi, etc. What we're wondering is how the timing of our arrival will affect our ability to gain admittance to any of these schools. In the U.S., for example, admission to competitive private schools is a year-long process, and the incoming classes are usually set by now. I've written to the schools themselves about this through their contact pages, but none have responded as of yet. Any insights on this are hugely appreciated!