Yoma 17: The Kohen Gadol Eats First

The layout of the Temple - a contradiction between a mishnah in Tamid vs. one in Middot. Is this a debate in methodology or in content? Also, the oral nature of the tradition may have had impact here. Also, a shift to focus in how the kohen gadol chooses his food first,from sacrifices, from lechem hapanim, even. The process leads to what appears to be a contradiction in terms, a neat resolution, and some questions on tying up the loose ends here.