I took the weekend off from this.
I wrote out the basic chronology of the emperor list, and filled it in with known emperors.
Caracalla us technically a third century emperor too, but in a sense your right.
Gordian III reign is closer to Valerians supposed reign of six years.
The pattern you noted, his ignorance of 3rd century emperors, nitpicked at me, as I'm searching for a source John Malalas would use.
Best guess is Lactantius "On The Persecution of the Christians".
He was also a philosopher, which I didn't know, and a major expounder of the modern concept of the end times, and a heretic to boot.
His list I saw for the emperor list DOES NOT INCLUDE the names of the missing emperors either, according to the list I just scanned from a questionable artical.
So.... It's might be a crucial source.