I think the best we can hope for is a diglossic situation such as what you find in the Arab world, where the difference between the Arabic used in the media and education is as great from that used in the streets as the difference between Vulgar Latin and the various Neo-Latin languages.
The problem is not so much the Reformation, but the growth of of a sophisticated literature in the vernaculars, which began before the Reformation but was contemporary to it, to a certain extent. That's why you need to butterfly away people like Dante Alighieri, Antonio de Nebrija, Jacques Lefèvre d'Étaples, and Miguel Cervantes. I think it's too much to expect that the people in the non-Romance speaking parts of Europe use Latin as a lingua franca, but perhaps Latin could continue to occupy the same role there as Arabic did in the Ottoman Empire and in Iran to the present date - as a language of culture and religion. That's not too far from the OTL - as far as I can tell, the last stronghold for Learned Latin (the academic dialect) was Germany, where treatises in Latin were still being published into the last century. In the rest of Europe, it strikes me that Latin publications were largely the province of the Church, but I could be wrong.