In our observance of second day Yom Tov when we continue the minhag of our forefathers even though we now have a fixed calendar and know very well which day it is. Gem Beitzah 4b.
The result is that in the musaf service for the second day of Sukkos outside of Israel, the musaf offering mentioned is the same as on the first day.
So we stand before Hashem and effectively say something like, “We are unable to bring the korban musaf for today. We should bring the korban for the second day of Sukkos, but Your sages taught us to treat this day like a sofeik first day and so we are only going to mention the korban for day one even though we know very well that today is the second day of the chag.”
I have been told that if we were to mention the offerings for both the first and second days, then we would be denigrating the holiness of the second day.
My question is whether there have been any proposals within Orthodox Judaism to mention the true musaf korban for the second day of Sukkos in golus.