Yoma 40a - order of avodah inside

It occurs to me that the order of the avodah inside the kodesh kodoshim is incredibly complicated; tangled, I would call it. Here's what I would have done:
Viduy on par, second viduy on par and shecht par, bring blood into kodesh kodoshim, then to paroches, then to mizbach hazahav.
Hagralah to choose sair. Shecht sair, bring blood into kodesh kodoshim, then to paroches, then to mizbach hazahav.
Scoop ketores and coals, bring to kodesh kodoshim.
Nice and simple: par all the way through, then sair, then ketores.

Here's what actually happens:
viduy on par [par], hagralah [sair], second viduy on par and shecht par [par], scoop ketores and coals and bring to kodesh kodoshim [ketores], bring blood of par to kodesh kodoshim [par], shecht sair and bring blood to kodesh kodoshim [sair], par to paroches [par], sair to paroches [sair], par and sair to mizbach hazahav [par and sair mixed together].
There is no way to have scrambled them together more thoroughly. Is there some reason why it has to be that way?
(Note that we also "scramble" the avodos inside and outside - garments gold, white, gold, white, gold.)

Note that in the fifth perek there is a long section ("חוקה") on how this order is actually מעכב, which apparently is not the case normally for most other avodah.