I don't play ottobros often so my time frame is off, but it's still roughly the same time frame for both approaches if you think about it, as you said yourself a good chunk of the land you get through missions.
The fear of colations is not a concern as ottomans, because frankly the only people who can stand up to you are Austria or a bloc of muslim powers, both of which rarely join up just by taking Byzantium lands, the people who ally them the most early game are serbia or Bosnia who are hardly a threat.
All your other points though I wont' contest since It's a matter of personal taste from there, I don't agree with ottomans westernizing because I think it ruins some of the challenge for them, I also just don't like the idea of byzantium existing period, I like to see them die ASAP.
I will argue however any "gains" seen with vassalizing byzantium are minor and your time is better served taking the land ASAP, converting it, and using it right away to get dem buildings/naval forcelimit up
The issue with coalitions isn't the fact that you can't beat them - that's easy. You avoid coalitions for two reasons: it takes longer to beat them and you get a lot more for your warscore if you beat up on regular alliances. So a coalition forming is to be avoided simply because it makes things slower (and somewhat harder, although by no means impossible especially as the Ottomans). And since you argue not to westernize as the Ottomans I suspect you're not arguing in terms of effectiveness here, which obviously turns everything into a matter of taste - not to belittle your play-style, I myself often roleplay or set myself specific goals too.
But if we're talking effectiveness and best investment/reward ratio both vassalizing Byzantium as well as westernizing is at the better choice. Westernizing as the Ottomans takes about 7 years and costs about 3.000 monarch points. Since you have a -25% tech penalty that's +150 MP / tech you pay more. Even if we completely ignore the fact that western units will mop the floor with the Ottomans by the 1700s (even if you manage to keep up in military tech which is entirely doable ofc) your invested monarch points will have paid back after 20 tech levels. There're roughly 90 you can buy - it's simply a no-brainer.
The only argument against westernizing is the ability to vassalize Indian and Chinese tech group nations if you stay Ottoman. That is easily exploitable though since you can pretty much stomp through India and China and be mostly finished by 1600, westernizing right after that. So, for all it's worth, play the Ottomans however you like it best - but if you want to maximize your game-play, both vassalizing the Byzantines and westernizing are the hands-down better choice.