From Unmoved Mover to Eternal Mover

Thomas Aquinas, building on arguments found in Books 7 and 8 of Aristotle's Physics, argues in The First Way (in Summa Theologiae I q2 a3, and in a parallel passage in Summa Contra Gentiles I.13) for the existence of an unmoved mover. However, there is an evident gap between such an unmoved mover and God. At the very least, Aquinas needs to show that the unmoved mover is absolutely unmovable (in all respects). If he can establish that, then he can conclude that the First Mover must exist outside of time. And, in order to exist outside of time, the First Mover must lack all passive potentiality (i.e., be a being of Pure Act).
 
Aristotle and Aquinas are both well aware of this gap, and they have a definite strategy for filling it. The argument goes something like this:
1. Assume (for contradiction) that the First Mover is changeable in some respect.
2. Necessarily, time passes if and only if change occurs.
3. All motion in fact depends on the activity of the First Mover (established by the main argument of the First Way).
4. If the First Mover were changeable in any respect, then it could be in a state in which it failed to cause any motion.
5. To be in such a state, the First Mover would have to be in that state for some period of time (since nothing can be in a state in a single instant).
6. Since all motion in fact depends on the activity of the First Mover, if the First Mover were in a state in which it failed to cause any motion, there would be no change during the period in which it is in that state.
7. If there were no change during that period, time would not pass during that period.
8. If a period has a temporal duration, time must pass during it.
9. There would be a possible state of the world during which time both does and does not pass. Contradiction.
10. So, the First Mover cannot change in any respect.
 
The crucial premises are 4, 5, and 6. Let me take 5 and 6 first.
 
Premise 5. This is based on Aristotle's resolution of Zeno's paradoxes in the Physics. Instants of time are not parts of time--they are only boundaries of such parts. Hence, nothing happens during an instant. Nothing can be in a state of activity or inactivity for only an instant. Instants can only mark the beginning or end of a period of activity or inactivity.
 
Premise 6. This depends on a kind of subtraction principle. If all change in the actual world depends on the First Mover and there is a possible state of the First Mover in which it would cause no change, then there is a possible world where no change occurs. We can simply subtract the activity of the First Mover from the actual world without being forced to add any new source of motion.
 
So, the crucial assumption is premise 4.  Suppose the First Mover is changeable in some respect. Why think that it must be changeable into a state in which it would cause no motion at all? Why couldn't it have a nature such as to cause motion in every possible internal state, while admitting of more than one such possible state?
 
There is some plausibility to the idea that the activity of a thing must depend on the thing's internal state, and that this dependence entails that there be some internal state in which no activity would result. However, this seems far from airtight to me.
 
I think there's a better strategy for defending premise 4--one that is not explicit in the texts of either Aristotle and Aquinas, but which lies quite close to their conception of time and motion.  If something is changeable in any respect, then it lies within time. If a thing lies within time, then its natural activity through time depends on the metaphysically prior passage of time. So, it is impossible for the activity of something changeable to be the ground for the passage of time itself. Yet, that is exactly what the First Mover must do. Hence, the First Mover must be absolutely unchangeable.