A partial answer, addressing only the question of the scapegoat on Yom Kippur:
Firstly, your assumption that this ritual was performed during the time of the Mishkan in Shiloh (as well as earlier times) is borne out by a beraita quoted in Yoma 67b:
המדברה המדברה במדבר לרבות נוב וגבעון שילה ובית עולמים
“Into the wilderness” (Leviticus 16:10), “into the ...
The Ramban al Hatorah, here says that there were no Mussafim on the Yamim Tovim in the Midbar.
The Nissuch Hamayim is very complicated as the Gemara in Taanit says that it is permissible to be brought at night.
Korbanot can not be brought at night. Does that mean that the Nissuch Hamayim is not an Avodah, or it is and it has an exception?
This does not ...