yes.
How do you solve the problem this creates of lack of economic development collapsing your stability?
It's hard. You need some luck too. If you expand into Asia minor, there is a lot of stability to counter the Balkans. Don't ever raze cities and have good rng with the barbs on the east front. Byz's collapse time matters too. Although you have little influence on it.
This still happens and is really, really frustrating. Yes, there was an IRL collapse of the Ottoman Empire during the Timurid invasions. Is it cool to simulate that? Yes. Is it cool to then make the UHV impossible if this happens? No.
have you tried to postpone the conquest of Anatolia until you conquer the balkans and Egypt first?
Balkans, yes. Egypt, no. Maybe Egypt is the key. Conquering the Balkans first is even worse, because they are contested territory rather than core or solid territory.
Stability will be an issue at times. To make things better trade for luxury resources to improve happiness in the cities as some of them may be unhappy and make some manor house here and there. Plus go straight for Constantinople, so that you change capital only once. In my personal recollection of scoring the UHV Egypt is the key, just remember you need to control all cities of a province, one is enough as long as no other player control others located in such province. Which means raze all cities in Egypt but one.
Stability is ALWAYS an issue. I've never seen it not be since the upgrade from several years ago. This is exactly the problem, and why I'm so very frustrated with this particular civ. From prior experience, I always beeline for Constantinople. I tried a couple times. The game I just did last night and this afternoon was actually going well. Conquered the entire Balkans, Anatolia, Rhodes, and Cyprus by 1452. No unhappy cities, manor houses in all but the most recent conquests, plus some courthouses and castles. Sounds great! And then two turns later, the empire collapsed. I'm done. This was on Viceroy difficulty, BTW. And I was effectively conquering cities every other turn, and barely squeaked by getting the UHV. So I'm gonna call it and say that this Civ is broken. Again, the Ottomans DID collapse under the Timurids. But, if a collapse happens in RfCEurope, which it always does, then you lose. Maybe some people don't play games to have fun, but I do.
