Many IEists, like Jay Jasanoff for one, feel that the reduplicated perfect is not really reconstructable for PIE per se but rather that it carried some other function, perhaps a kind of iterative meaning much like its close kin, the reduplicated present (e.g. *di-deh₃-ti 'she gives'). The reduplicated present displays what is often referred to as i-reduplication in order to distinguish it from the e-reduplication seen in the perfect forms. So far, I've been explaining away i-reduplication as a reflex of former schwa in preaccented syllables in early-to-mid Late IE. Simply put, an original *ə would have been 'sandwiched', so to speak, between two consonants resulting over time in the increasing closure of the vowel (aka. increasing rise of the vowel) from generation to generation. A schwa that rises eventually becomes a high-central vowel, /ɨ/, which would be hard to distinguish acoustically from its preexisting fronted counterpart, *i, of known PIE phonology. Hence, I believe that schwa in preaccented syllables eventually merged with *i without much fuss.
I had up to now been explaining e-reduplication in like fashion. I had presumed that both forms of reduplication originally involved a schwa and that perhaps the only original difference between the two reduplications was a matter of syllable boundary. So, perhaps i-reduplication was the result when the schwa was placed in an open syllable while e-reduplication was the result when the schwa was in a closed syllable, or perhaps vice versa. I admit, while clever if I do say so myself, it's a little more ad hoc than I would like. I can't think of a way of proving such a thing.
However, I came to realize that if, for whatever reason, the e-reduplication seen in the eventual perfect forms were not as ancient as the i-reduplicated forms seen in the durative present, then perhaps we could suggest something simpler:
Perhaps while i-reduplication is inherited from Mid IE and has not undergone loss of original-schwa-turned-*i in its reduplication due to an exemption to Syncope grounded in straight-forward phonotactic restraints, reduplication of the *bʰe-bʰor- kind which originally would not have had a perfect function was coined quite late (i.e. during mid Late IE, perhaps concurrent or postdating my Schwa Merger rule when preaccented schwa merged with *i) and was using *e as a reduplication vowel right from the beginning!In this way, I no longer have to muck around with open and closed syllables or an ad hoc reflex of schwa as *e on top of *i. Instead, preaccented schwa simply becomes *i. End of story. It certainly tidies things up (i.e. Occam's Razor likes it) but I will have to ponder on this some more. Perhaps my readers may be aware of an important detail I've overlooked that negates these possibilities.