I agree, I also wouldn't want the Ottomans any easier, the challenge them being strong in general is fine by me. I also agree with your strategy 100% but what did not work for me with this exact approach were my allies:
I had two games as Knights, both times the Ottomans were busy in the east, their manpower was down to something like 3 to 4k, I had naval superiority and my allies started conquering / sieging the balkans (first game allied to Austria, Papal States, Venice; second game allied to Austria + vassal Hungary, Lithuania, own vassal Byzantium; both times outnumbering +full manpower!), but when the Ottomans arrived (I didn't manage to siege down the straits fast enough because of coastal landing and attrition bringing down my army from 11 to under 9k), they picked them apart one by one. My allies were in separate smaller stacks (max 18k, most 8-12k), never merging, always avoiding battles / fleeing, breaking off sieges, wouldn't join battles (though that would have resulted in superiority in numbers). There are already some threads describing this phenomenon, where allies won't help in any significant way if they come to the conclusion that they would loose the battle on their own, they simply ignore the possibility of combined strength.
I read somewhere that it might confuse the AI if you set targets, that are behind forts, meaning "not reachable" for the AI, so they act uncoordinated. I will try to select bordering provinces first to draw the allies closer together, but I don't have much hope this might help.
Another point was, that the Ottomans were at military tech 5 (me as well), while whole Europe was still at 4 although renaissance was already wide spread. This might have supported the AIs calculation to better not engage the Ottomans armies, but still, while outnumbering the Ottomans, all my allies wouldn't achieve anything useful. Needless to say while fighting all these small stacks, the Ottomans grew in numbers (both with new regiments and increasing manpower).
EDIT: Todays Dev Diary talks about "allied AI behavior" as one of their gameplay topics they might work on, since "now the AI acts on its own interests, which may not be the player’s". So eventually the described phenomenon could not be wad.