Looking at this in different editions, you find μεμειχμένα in Lobel-Page, Voigt (whence the above snippet), and Campbell, μεμειγμένα in Edmonds, and μεμιγμένα in Bergk. None of those offer any "original form", that is none of them tells us what was readable in the tradition. From Voigt, I infer it could have been παντοδάπαις* μεμ*ιχμένα χροίαισιν, with the stars being any letter group subsequently amended to the contents of Voigt's angled brackets. But then the critical note has «-χμ- L.», suggesting the chi was Lobel's suggestion. So what was actually in the tradition? And why tamper with that participle if, as Bergk would suggest, the tradition reads μεμιγμένα, which AFAIK is the correct form of the perfect participle of μίγνυμι? Would the other forms come from other verbs, or am I missing something about μίγνυμι's conjugation? And if the tradition was indeed παντοδάπαις μεμιγμένα χροίαισιν, why force it into book 2 when a simple diaeresis (χροΐαισιν) would put it in book 1 and the quoter doesn't tell us what book this is from?
The old books about Aeolic have now been thoroughly superseded by:
not yet (it seems) available as a published book, but you could approach the author with questions.
Angle brackets normally mean editorial addition, which strongly implies that the stars in your reconstruction are empty: παντοδάπαις μεμιγμένα, with the App Crit saying that μεμειχμένα was Lobel's idea.
Lobel's emendation in turn is because there is evidence that the Aeolic form of the verb is μείχνυμι: per LSJ, both ὀνεμείχνυτο and ὀνεμείγνυτο show up as readings in Fr. 44.30. The catch is that ὀνεμείχνυτο may also be Lobel's emendation of the more regular ὀνεμείγνυτο there, so Lobel may be drawing both emendations from some other source.
Right now, I know that the source exists, but I can't pinpoint it with free online materials. The 1909 edition of Thumb's Handbuch der griechischen Dialekte does not mention μείχνυμι: https://archive.org/details/handbuchdergriec00thum . The 1959 edition, which is not free online, does, as the Google search snippet shows:
Βemerkenswerte Ρrăsenssta mme, δείχνυμι, μείχνυμι s. 8 255, 14; statt αποδείκνυμι das einfache Verbum: δείχθεις χελληστυάρχας mehrmals aufΙnschr. Gegenüber thess. βέλλειτει, boiot. βειλόμενος heiβt es βόλλομαι (Sa., Αlk., Τheokr. ) ...
... I just hope that it has more evidence to bear than "because Lobel said so". I have a copy of Hamm, Eva.-Marie. 1957 Grammatik zu Sappho und Alkaios, and I will look it up when I go home. Stay tuned; as is our tradition with Sappho answers here, there will be a few iterations.
UPDATE: I haven't looked it up yet, but if Lobel did introduce μείχνυμι into the text without manuscript warrant (which I don't know yet), he presumably did so by appealing by analogy to the form δείχν-, which DGE reports for "Alc.73.13, 303Ab.14".
(Unless Lobel made that up too. I'm worried whether the grammars adequately differentiate between the words in the manuscripts and editorial conjecture.)
why force it into book 2 when a simple diaeresis (χροΐαισιν) would put it in book 1 and the quoter doesn't tell us what book this is from?
Because we're taking plenty of liberties with the source as is, and the conservative thing to do is not to posit a diaeresis unless the original reading is clearly not acceptable.