does the augment not exclude that it is a reduplicated aorist?
I'm not sure why it would in the indicative. Aorists typically have augment (or sometimes not, in Homer). The reduplicated aorist infinitive πεπιθεῖν would not have augment, of course. But ἤγαγον, from ἄγω, has both reduplication and augment.
παρμέμβλωκε -- the root is μ-λ, as shown by the aorist ἔμολον, but in forms where there is no vowel between μ and λ , β develops "epenthetically", giving the reduplicated perfect form μέμβλωκε. In the present βλώσκω, the consonant cluster μβλ- is reduced to βλ- at the beginning of the word.
Another example of this process of epenthetic development of β between μ and a liquid is ἀμβροσία, the food of the gods, or immortality generally. This is from ἀ-μροσ-ία, where μροσ- (probably from μροτ-) is etymologically derived from the same source as Latin mors
, etc., Russian u-meret'
Also ἁμαρτάνω-ἤμβροτον. ἤμβροτον is the epic form; Attic would be ἥμαρτον. ρο (as well as the smooth breathing; Aeolic was psilotic) marks ἤμβροτον (and ἀμβροσία, too) as Aeolic. ρο is the Aeolic reflex of an earlier "syllabic" (vocalic) /r/ ("ἥμρτον"), which becomes -αρ- in Attic-Ionic. Aeolic forms are generally preserved in Homer in formulas where the Ionic equivalents had a different metrical shape and so could not replace the Aeolic forms.