You have done everything i your power to avoid having good conversion throughput.
And you dont have to convert much, Humanist and all that.
If I wasn't going for 1 faith as Ottos, I'd have gone humanist and just right-clicked that conversion reminder away to save tons of hassle. You don't have to convert ANYTHING once you have it. IMO not even worth since you'll never keep up and thus will need to keep OE below an actually still-high threshold to avoid rebels everywhere instead of just borders.
Assuming high legitimacy (with strengthen government + Ottoman government you should have it) and nothing but humanist, heathen provinces contribute 100% to unity and heretic provinces contribute 75%...there's no possible combination of provinces (including 0 true faith) that would put you below 100% unity and religion would be giving you mostly -3 unrest.
If one goes revolutionary as a nation like this, all provinces give at least 3 tolerance and -2 unrest (from humanist) without exception and you're locked at 125% unity. This is before stab, theologian, temporary decisions, or the -unrest from legitimacy or RT itself. It also ignores policies or a late game 7th idea group dump into plutocratic (from rev republic) for another -2 unrest.
Humanist Ottomans in the late game can easily tank > 160% OE in wrong culture, wrong-religion provinces if they don't have separatism...and like you said they don't have to do so to 1-tag. Definitely the way to go if you value sanity on these runs.
That said, if you do want everything to be Sunni you take religious and swat the resulting rebels in border provinces away. No need for humanist, not with unify Islam and everything at true faith. It's annoying to convert thousands of times but plenty doable...and Christian Ottomans actually convert faster in the late game. Even with rev government losing me a little piety (lots of late game wars so 100% is quickly restored) and DotF missionary 1-faith was only 5 years after 1 tag.
For some religions, heathen tolerance is by far the preferable path (Tengri, Hindu, Fetish, Confucian) as these religions are terrible for conversions and going religious with them would be akin to variant/challenge play.