The point about acknowledging debt is just that EY apparently went in with the intention of publishing something within range of JKR's copyright. This would speak against an argument that the intention was parody: if the original intention were fair use parody, then why the legal disclaimers at the heading of each chapter?

Parody is by definition 'within range of JKR's copyright'; anyone wanting to write a parody is going in with that express intention. Attribution is just common courtesy and useful metadata. Per my previous quotes, this probably only would matter to the judge as indicating that the author's intent is not malicious.

If that was out of respect only, then why the word 'disclaimer', and why stop doing it after JKR had given legal permission to FF writers?

JKR hasn't given legal permission, she's merely made some intent clear which at most, from what I recall of my classes on the topic, gives fanficcers a weak promissory estoppel. Why stop? Because he did it a few dozen times before, and the purposes have been served.

Some MoR chapters point out absurdities in JKR's work, but EY doesn't make it his business to lampoon the original series. Judging from the wiki page on fair use, this makes MoR a 'satire', and these fare much worse in fair use cases.

Exclusively focusing on criticizing canon is not necessarily helpful; original content helps pass other criterion like being a transformative use of the original and not being a replacement but a complement:

The Ninth Circuit also found Penguin's use of The Cat in the Hat non-transformative based on its conclusion that Penguin made no effort to incorporate "new expression, meaning, or message" into the secondary work.323 As a result, because market substitution was more certain, the court was willing to infer market harm under the fourth factor. 324 The Ninth Circuit, in its failure to analyze what would constitute "new expression, meaning, or message," at the very least, missed an opportunity to clarify the nature of a transformative work. This consideration was important because if The Cat NOT in the Hat! was transform ative , the first factor may not have weighed against fair use, despite the commercial character of the infringing work.325 Additionally, market substitution would be less certain and market harm might have been less readily inferred.326

...The Ninth Circuit cut short its analysis, or at least any presentation of its deliberations, regarding whether The Cat NOT in the Hat! was transformative.351 The court did not explain how the new work failed to incorporate original expression, meaning, or message.352 The court also failed to indicate how this new work would have superseded the original work.353 A full consideration of these subfactors under the analysis of purpose would have led the court to recognize the new work as transformative.354 As a transformative work, The Cat NOT in the Hat! could have been considered a fair use, after a full examination of the other statutory factors. 355