That assumes that they are doomed to decline regardless of butterflies. If they can continue to produce quality Sultans they may be able to stave off serious decline for quite some time. The rest of Europe will rise in relative power but who, how and when may change.
In my opinion the idea that the decline of the empire was caused by poor Sultans is a product of misunderstanding of the Ottoman system and nationalist Turkish historiography that has tried to discount the entire Ottoman period after Suleyman.
The reality is that the empire was just too big with too large a machinery of government to be run by one man. While individual sultans could have a negative impact on the functioning of the empire, the causes of decline were really not personality-driven but rather due to economic forces beyond the empire's control.
The empire was massive, but that masks the relative poverty and environmental vulnerability of most of imperial territory, which is largely arid or semi-arid, and was sparsely populated compared to Central and Western Europe. It was really the early-Ottoman military superiority that allowed the empire's rapid rise, and once that eroded, you essentially had a sprawling and poor empire versus rich and populous European countries.
In this TL, the Ottomans control Italy, which is of incalculable economic value to the empire, and leads to an Ottoman presence in the New World, which would ameliorate many of the economic causes of decline, which were largely inflation due to New World precious metals, and the rerouting of trade away from the empire.
