The French and English and Dutch only came along in the 1600s and the English and French only really made headway in the early 1700s.
The Turks would do business after Constantinople fell, but for a price; Europe was simply looking for way to bypass them, as you mention. It wasn’t until 1492 that the last Muslim bastion in Spain fell.
When you look at how Spain holds on in Morocco (cities along the coast, like Ceuta), I’m surprised that the whites in South Africa didn’t attempt something similar: stake a claim on land (preferably along the coast for security purposes), and live in a 100% white country rather than attempt to govern as 10% in a black country. Even the part of Morocco that Spain left (”Western Sahara”) is resisting Moroccan claims - they insist that Morocco flooded them with settlers to skew any balloting.