Very lovely little package there.
I too very much enjoyed "I am king not by grace of God, but by my own splendor!" All hail King Anton Szandor LaVey!
But...eh...my two cents. *Ahem*
The Enlightenment was really only possible
because of, not in spite of, the monarchial tendency toward religious fanaticism. Religion + State = Bad. (Very simplified. Very, very simplified.) Religion dictates that this guy is king because God says so. One king in heaven, one king on earth, etc. Religion dictates that this other guy is a serf because God says he is a serf and must ensure the longevity and power and glory of God's representative (ie, the King) in France, Prussia, Austria, Rome, etc.
Therefore, if you suddenly have a bunch of Western European monarchs adopting the Enlightenment's ideals of egalitarianism and fraternity, the very structure of society and government must be rethought. You suddenly have the French Revolution butterflied away. Louis XIV ruling by his own splendor must have a reason why he is better able to lead than that serf guy, and the metaphysical explanation of divine right and blue blood suddenly doesn't cut it. So he needs to garner popular support which means curbing the excesses of the French court and allowing the puppet National Assembly some actual power, or he'll go the way he did IOTL the same way that Nicholas II did.
Therefore, you have enlightenment-influenced governments as early as the seventeenth century progressing towards a new paradigm by the 19th century, and the major upheaval that was the French Revolution doesn't offer the Church a catalyst to rail against the Enlightenment.
Vis-a-vis, Enlightenment must be inherently anti-religious (or at least anti-establishment) for the Enlightenment to even exist, and any existing monarchs suddenly embracing the Enlightenment, especially the French monarchy, would butterfly away the late-18th century revolutions except in the most extreme cases.
Now, a very plausible case would be in places in Northern Germany where Catholicism, being the minority, was still devoutly practiced yet heavily persecuted. You have the industrial revolution making things miserable for everybody who isn't a landowner, especially minority groups. Let's push the revolutions of 1848 back a little bit to....say.....1830. This same year you have the Polish rebellion against Russia, the French invasion of Algeria, and the recognition of an independent Belgium. Lots of things going on around Germany that prevent any outside aide to flow in to put down the revolutions. Now we prolong the revolutions beyond a single year and let's say by 1835 you have the successful establishment of a Catholic German state in Northern Germany (it'd be small and probably would cause another big old European war prior to WWI and definitely would affect relations between Germany and Austria later). One of its war-heroes or the first president or some such institutes democratic institutions, works for social justice, and promotes the cause of Catholicism both at home and abroad. Miracles are attributed to him, and badda bing badda boom, you have some one revered within the country though he would probably be canonized only in the 20th century. But still, he'd be the
de facto patron saint of this country, and under the great democrat himself Pope John Paul II, he could very well become the
de jure patron saint of democracy.