Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
This is a complicated issue of history, specifically because of the situations for academic and professional study of history in Ethiopia in relation to the past 4 decades, which have seen an exponential growth in the professionalization and sophistication of the study, but also a level of devastation not seen in Ethiopia since perhaps the Ahmed Gragn in the 16th century.
But today there is a growing relationship between Egypt and Ethiopia, but ecumenically and academically, which is yielding quite a bit of fruit, especially in the fields of manuscripts and texts. There is in fact a flourishing revival which should help out quite a bit to solve these very kinds of questions, especially considering how even despite many catastrophic periods of cultural destruction of manuscripts, Ethiopia remains one of the world's treasure troves of ancient and lost texts.
In Ethiopian tradition, the Rites of the Church, and the 14 Anaphoras (Qurbon
in Ge'ez/Amharic) and the Liturgy (Kidase
in Ge'ez/Amharic) are seen as revision
of foreign and indigenous sources, which are taken from their originals, but distinctively Ethiopianized in the process quite familiar to Ethiopian scribes and translators. Ethiopians rarely if ever translate things literally but rather include the flair or indigenous language and cultural aspects into manuscripts and texts. This especially compounds the problems of identifying which aspects of manuscripts are indigenously Ethiopian and which are from foreign sources, and to which degree are they transmutations of both. This is also made difficult by the complexity of the Ethiopian written language, and also the particular flavor of Ethiopians to prefer cryptic and poetic writings/translations, as epitomized in the dual meanings of the Wax and Gold tradition of Qine poetry (where dual meanings are encrypted in the written versus pronounced forms of poems/writings that can only truly be observed by well trained linguistics who are quite well-read).
In regards to the specific Anaphoras, as already mentioned above, only that of Saint Basil is near verbatim, and even it has subtle differences from my experience with both the Coptic and Ethiopian services (I am quite mutual and active within my local Coptic parish). The Ethiopian liturgy, much like other jurisdictions is a complicated interaction of several variables and makes it very hard to pinpoint a lot of it. It is much easier to dissect and find pieces and parts that are parallel, and in Ethiopian Church writings there are many of these. In reality, it is very hard to find any obvious parallels in the worship services and traditions of the Ethiopians and the Copts, despite the past 1600 years of our mutually intertwined history.
Here is a link to audio files of all these respective Anaphorashttp://www.ethiopianorthodox.org/churchmusic/liturgy.html
Oh yeah, and by the way my Father-Confessor worked and is working on the revisions for the PDF file of the Liturgy book posted above, I helped out a bit on some more recent revision work, that is becoming the official "English" version of the Ethiopian Liturgy book and canon, but as you can see, it has been a 50 year process!