This question and particularly my comment on the question got me thinking. Assuming those who became the Ethiopian Jews received the oral law exactly the same as the rest of Israel, could we potentially use Ethiopian oral traditions to resolve machlokot that arose later in the Tannaic and Amoraic periods and were recorded in the Talmud? If this is theoretically possible, has it ever been done? If this does not work for some reason, why not?
My reasoning, if it's unclear, is as follows. If some point about a Torah law is undisputed in the Talmud, it seems to me that we would have a high degree of certainty that that point was successfully transmitted through the generations without ambiguity. If Ethiopians had a machloket about that point, we would be relatively confident telling them which side is correct. Is this logic reasonable, and does it work the other way around?
I originally neglected to mention that this question only applies to deoraita commandments, and not derabanans. Obviously machloket in derabanans is not a result of ambiguous transmission from Sinai that Ethiopian Jews could plausibly have more clarity on than the rest of us.