"It is erroneous to look at 19th century as a period of change and the pre-1800 period as one during which many East African societies were static." Discuss.
There's basically no such thing as a static period in history. Things are always changing; it's simply a matter of degree. Compared to the rapid change of today, almost any historical period is going to seem stagnant. Since the Industrial Revolution, the pace of technological, economic, and political change has increased, and continued to do so until it reached breakneck speed in the 20th century. (It may finally be slowing down in the 21st. Maybe.)
Unfortunately almost all the only good records we have from pre-1800 East Africa are from European sources, which were beyond biased. They depicted African people as violent savages, barely above animals. We know this isn't true, but unfortunately it's very difficult to know what life was like in African cultures during that time, as hardly anything was written down by indigenous populations.
So what we do know is as follows:
Starting around 1460, Portugal conquered territory in Africa and established the slave trade. During the period from 1600 to 1800, Portugal begins to lose its dominance as other European (mainly Dutch and British) colonists conquered territory in large swaths of Africa and dramatically expanded the slave trade, establishing the "triangular trade" network where goods from Europe (especially guns and alcohol) are brought to Africa, used to buy slaves, then brought to North America or the Caribbean to be sold for other products such as sugar cane and tobacco that are then brought back to Europe. The merchants made a profit at every stop along the way.
Also important especially during the earlier part of this period was Ethiopia, one of the first Christian cultures in Africa and for a time a significant world power. Around the 16th century they began to decline, and then once foreign powers from Europe and the Middle East started taking over they fell apart completely.
Over the 17th to 19th centuries, the kingdom of Rwanda became very powerful, conquering a number of smaller kingdoms in the region. In the 17th century the Luba kingdom also became very important, in what is now Tanzania.
But for all we do know about what was happening in East Africa during this time, the really striking thing is how much we don't know; we've tried to piece it together with archaeological findings and what few records we can find, but it's not easy. One reason why it might seem stagnant to our modern eyes is simply that anything seems stagnant if you don't know about all the changes going on.