Well this has been a interesting chapter, I suspect at the end of the day it would be natural for the US and Ottomans to hostile to each other, USA being a nation of immigrants would inherit the attitudes of hostility towards the Ottomans, but well with little reason to deal with them besides the barbary pirates would stay hostile unlike Christian Europe who has to live with them, add them being a resurgent empire with a interest in Latin America, a counter example to the idea of full democracy being the greatest system ect I guess their bound to clash.
By the way I'm curious how the Ottoman identity will with ethnicity as time goes on, as well identity has always been complicated and specially with the rise of Arab nationalists I wonder if a counter will form loyal to the empire.
For example say in the case of the Kurds, with the exception of those in Persia they've been in the Ottoman empire for most of their history, their have couple of languages that don't really mix well with each other with Sorani being dominant in Persia, I wonder if you could have nationalists parties focused on their ''type'' being insurgents leads others of the same to veer into their Ottoman identity.
Such as say for Arabs the Arabs of Lebanon having already some control thanks to the French, vital port and strong connections to Europe would likely if they tried to rebel against the Empire would be opposed by the Arabs of Greater Syria.
I think you can kind of see it occur already with the Zionists in the Sinai as well given a lot of them are European Jews I think you could see Jewish Nationalism defined by Yiddish than Hebrew, well in their community.