Zevachim 89: Order of Operations

We begin with a Mishna:  Any offer that is more frequent will precede other offerings.  Thus the daily offerings precede the additional offerings (which are only sanctified on special days).  When the Shabbat and Rosh Chodesh fall on the same day, the additional Shabbat offerings are done before the Rosh Chodesh offerings.  The additional Rosh Chodesh offerings precede the additional Rosh HaShana offering.  The sources for this principle is stated regarding additional first-day of Pesach offerings in Numbers (28:23). It describes the morning burnt offering before the daily burnt offering.

A second Mishna teaches us that if there is blood of a sin and a burnt offering, the blood of the sin offering comes first as it effects acceptance or atonement for severe transgressions punishable by karet.  If lies of a burnt offering and portions of a sin offering are presented, the limbs come first because the burnt offering is entirely burned in the altar's flames while only part of the sin offering is consumed.   Both will effect atonement but the sin offering's blood is placed on the four corners of the altar and the blood is poured on the its base.  

The guilt offering is sprinkled on only two corners.  A guilt offering precedes a thanks and a nazarite's offering because of levels of sanctity.  A thanks offering an a nazarite's ram precede a peace offering due to the fact that they are eaten for one day while peace offerings are eaten for two days.  The thanks and nazarite's ram require loaves to be brought with them: four types with the thanks offering and two types with the nazarite's ram.

Sacrifice of the peace offering precedes that of the firstborn because the former requires placing blood on the altar in the form of two that are four and placing hands on the head of the offering, libations, placing hands on the head of the offering, and the waving of the breast and the thigh by the priest and the owner.  The firstborn offering precedes the animal tithe offering because it is sanctified from the womb and is eaten by priests, while all may take the animal tithe offering.

The animal tithe offering precedes the bird offering as it requires slaughtering while the bird's nape is pinched.  The blood presented on the altar and the portions burned on the altar make the animal tithe offering more sacred.  The blood of the bird offering only is placed on the altar.  They precede meal offerings because of atonement of blood.  The meal offering of a sinner comes before a voluntary meal offering because it atones for a sin.  The sacrifice of the bird's sin offering precedes the sacrifice of the bird's burnt offering regarding consecration as well.

As expected, the rabbis consider the nature of each of these statements - how do we know that one thing is more sacred than another?  This is a larger question regarding the current services.  What must be said first, second, third?