Learn English – “I’m not being” or “I’m not been”

Your pedant is completely wrong, not just because he's protesting in futility to a well-established idiom, but because his grammatical analysis of the construction is mistaken.

That being said is an adverbial participle phrase. Note that the verbal portion of the phrase, being said, does not contain a finite verb, and only finite verbs are tensed. (This is not just a fact of English, but a general facet of Western European verbal systems: non-finite verb forms generally indicate aspect and voice, but not tense.) The terminology is somewhat confused on this point since being is often called the "present participle", but there is in fact nothing that specifies the present tense about this construction, as the following examples show:

The lawn was being mowed yesterday.

The aquarium will be being cleaned all day tomorrow.

In all of these cases, the bolded portion does not contribute any tense information at all -- it rather indicates the progressive aspect and passive voice. The tense is entirely indicated by the finite verb in italics.

The idiomatic phrase that being said contains no finite verb and no tense. Your pedant has merely demonstrated his own ignorance of English grammar. There is absolutely no reason to object to this idiom.

I think that this sentence's problems start with the deadening and befogging use of passive voice. If I were trying to help readers understand whose interest in researching X is growing, who is investigating its applications to various fields, who has realized the desirability of "X which can directly deal with Y," and who desires it, I would recast much of the sentence in active voice. Because I don't know the various entities behind the growing interest, the investigations, the realization, or the desire, I must guess at their identity in my recast version. Here it is:

Academic interest in researching X has been growing in recent years, as researchers have investigated its application to various fields and as others have recognized the desirability of identifying the ways in which X can directly deal with Y.

By reducing the number of passive terms from four ("has been growing," "have been being investigated," "has been realized," and "is desired") to one ("has been growing"), my revision enables readers to grasp more clearly who is doing what in the sentence. The rewrite also renders the verb tenses simpler and more coherent.