I think I'll give this a try. Let's start with what a simple non-introspective mind might do:

Init (probably recomputed sometimes, but cached most of the time): I1. Draws a border around itself, separating itself from the "outside world" in its world model. In humans and similarly embodied intelligences you could get away with defining the own body as "inside", if internal muscle control works completely without inspection.

Whenever deciding on what to output: A1. Generates a list of all possible next actions of itself, as determined in I1. For human-like embodieds, could be a list of available body movements. A2. Computes a probability distribution about the likely future states of the world resulting from each action, consulting the internal world-model for prediction. Resolution, temporal range and world-model building are beyond the scope of this answer. A3. Assigns utilities to each considered future state. A4. Assigns preferences to the probability distribution of futures. This could e.g. use Expected Utility or some satisficing algorithm. A5. Chooses the possible next action with the most-prefered distribution of futures. Tie breaking is implementation defined. A6. Execute that action.

As part of A2, the reactions of other intelligent entites are modeled as part of the general world model. This kind of mind architecture does not model itself in the present; that'd lead to infinite recursion: "I'm thinking about myself thinking about myself thinking about ...". It also wouldn't achieve anything, since the mind as instantiated necessarily has a higher resolution than any model of itself stored inside itself. It will, however, model past (for lost data) or future versions of itself.

The important point here is that this mind doesn't model itself while computing the next action. In the extreme case it needn't have facilities for introspection at all. Humans obviously have some such facilities. Either inbetween deciding on output, inbetween the individual steps A1-A6, completely in parallel, or some combination of those, humans spend cputime to analyze the algorithm they're executing, to determine systematic errors or possibilities for optimization. I'll call the neural module / program that does this the introspector. When introspecting a thread which generates motor output (A1-A6 above), one (very effective) assumption of the introspected algorithm will always turn out to be "My own next action is to-be-determined. It'd be ineffective for me to run a model of myself to determine it.". For a mind that doesn't intuitively understand the self-reference and infinite-recursion parts, this turns into "My own actions can't be modeled in advance. I have free will.".

In the cases where the introspected thread is running another instance of the introspector, the introspector still isn't attached to its own thread; doing that would lead to infinite recursion. Each introspector will work similarly to the motor-output-choosing algorithm described above, except that the generated output will be in the form of new mental heuristics. Therefore, the same "It'd be ineffective to run a model of myself to determine my next action." assumption in the algorithm can be observed, and "Free will." is still the likely conclusion of a mind that doesn't understand the rationale behind the design.