Elturgard was formed in the 15th century. Elturel was older. Elturgard is formed when Elturel and it's Hellriders begin to take other towns and societies in the Heartlands under it's "guard", which starts
From your link:
In the late 15th century DR, it was the capital of the realm of Elturgard
By the late 1430s DR, through a variety of excuses, Elturel had laid claim to the lands of its neighbors, placing them within "Elturel's Guard" as they called it, making itself a petty regional power
That in turn only happened because of the fall of Scornubel as a major trading hub due to the Spellplague, which occured in 1385.
I see it as the Hellriders being around already, which they were. They're coming from Elturel, as mentioned.
So we have this notice written by someone essentially saying, "Hey, there are these guys riding around. They call themselves the Hellriders, and they're speading the message of a place called Elturgard, which I've never heard of, and I don't acknowledge."
To me, that means the idea of holy Elturgard was around, but wasn't officially acknowledged past the lips of a few militant riders. Some years later, the kingdom would become official on maps.
Basically, it's all plausible stuff from the year 1371. There's no need to dispute the date that Moonhaven fell.
The dated Dark Journal of Ilyn Toth is all that's needed to establish the year.