If Ballologists exist, what they practice is ballology or... ballologism

Perhaps, themilum. I did grant that there is place for "battologism" in the language, at least arguably, altho American Heritage does not appear to see a place for it.

But, in any case, if "battologism" is a word, it does not mean the repetition of the same words or sounds within the same phrase or sentence. It means the repetition of sentences saying the same thing in the same way or different ways.

That's a "battologism", themilum.

It's my pleasure to set the record straight for you ... again. If I have to say this again, some will think me battological.