gleaf, I do not totally agree with your analysis, though I appreciate your thought process since you have to model the behaviors in serial. (Or so it appears).
Tasks and skills unique to instrument flying are suceptible to clumping and grouping, typically in most easily clumped or grouped aggregates of 3 to 5. Once you get over five, you can typically clump or group the greater number in to 2 heirarchies of three, and so on. I'll suggest to you that it is indeed multitasking when you are actually flying. When you are watching the plane fly, maybe not so much.
That disagreement aside, you are on to something in terms of serial prioritization, which we list as the holy triumvirate in aviation:
Aviate
Navigate
Communicate
Inside "aviate" are a lot of sub tasks, some of which you do in parallel when flying, some in series. You can talk and fly at the same time, that need not be done in serial, and you can also navigate and fly at the same time: many of us have done so. The reason we fall back to that holy triumvirate is to make sure that as we encounter changing conditions or changing requirements, we take care of first priority when task loading increases. Malfunctions and emergencies are typically a period of increased task loading. Responses are typically organized around the prioritization logic of the holy triumvirate.
Things get a bit more complex when dealing with change while operating under instrument conditions. (It's easier to do when VFR, since you peripheral senses help you with flying references ...)
As far as multi tasking, breaking down an instrument scan would appear to be a serial exercise, as you alluded to. One typically trains an "in order" priority of condition and task decisions by going from your primary instrument, the attitude gyro/artificial horizon/whatevertheycallitnow and then cross check your various performance parameters: airspeed, altitude, vertical speed (if any), heading, power, ball in, time, fuel, etcetera. The core conditions to consider are pitch, roll, and power, by which your aircraft's performance (flying) is governed.
Ab initio instrument training typically brings you back to the vertical gyro's display between each cross checked instrument, however, there are other effective instrument scans (NASA had a circular scan that better followed muscle movement in the eyeball) that for my money is more effective.
An instrument scan is "a rinse and repeat until conditions or performance changes," repetitive task. You switch to a tailored scan pattern suited to your task should your task be other than flying straight and level:
climbing turn, navigational problem, speed and heading change, configuration change, and so on.
You do this while dealing with all other matters within the aircraft in parallel, and are frequently (particularly when flying as a single pilot) multi tasking: doing several things at once.