If my memory serves me right, the validity/veracity of "AnIya nIla shRRi~NgAt" / its authorship by Swami Desikan [either/both, need to rehash memory from the old discussions] was questioned a long while back.
Just wish to make a note that YPP quotes it and calls an abhiyukta's. [The AndhrapATha of the grantha is missing this episode, fwiw]
Now, the context of the source set, one does also need to consider that YPP again adds a parItApI that could be considered by one to set the date in stone to circa 1372/3, in effect placing it beyond the dating of Swami Desikan.
But, the concern there is as such, how the structuring is with the same sentence - a loosely gathered phrasal construct. Add to that koyilozhugu claiming it a 1293 saka - parItApI, and the different afflux between a Gregorian boundary and the Saka one.
This should be a good one to sit with sometime soon, to ascertain further specifics.