As I understand it, Columbus set sail to America in 1492 because trade with Asia was being heavily taxed by The Ottoman Empire, and so Europeans were compelled to find a different route. But The Ottomans didn't capture Jerusalem until 1516, so why didn't European traders just pass through there instead?
Well you actually came upon a historic misconception, and the main argument in proving the misconception wrong
I talked about it in much detail here, but to recap briefly. The idea that Europeans started searching for a different route because the Ottomans blocked or heavily taxed the previous route isn't borne by the data we have.
In fact the opposite is more true, throughout 15th century Europeans (mainly Venetians, but also other Italians, French, Catalans, etc) were buying massive amounts of spices in Egypt (Alexandria) and Levant (Beirut) - which were Mamluk controlled - and were in fact the main trade hubs for spices where overwhelming majority of European spices was bought and we see no discernible interruption or change in this pattern until Portuguese arrival in Indian ocean. Comparably to Egypt and Levant, Constantinople was the place where only a fraction of spices passed through and such was of negligible importance. I don't think Ottomans ever increased taxation or done any action to hinder trade, but even if it did it would not influence the major trade routes until 1517, as you yourself noticed.
Look into my previous post on the issue, and feel free to ask any follow ups here