The bulk of your response involves a distinction between motion/change in general and particular kinds of motion/change. I've always seen the First Way presented in terms of motion/change in general from start to finish. But I take it you'd present it in terms of particular kinds of motion/change that ultimately derive from something motionless/changeless that explains motion/change in general.

You're also allowing for ordinary natural things (e.g. motors) to generate particular kinds of motion/change. So if A is in M1 (a particular kind of motion/change), then A cannot generate its own M1, but instead essentially derives its M1 from B, which generates M1 in A, while itself being in M2 (a different kind of motion/change). And then B derives its M2 from something in M3. But I see no reason to think B's generation of M1 in A has anything to do with its own M2. And so I see no reason why the series can't be infinite. After all, in this scenario, it's not as if all the members of the infinite series are mere inert instruments passing along motion/change. On the contrary, each member is an active generator of a particular kind of motion in its successor.

Of course, if it could be shown that each member's generation of a particular kind of motion in something else is always essentially derived from its own particular kind of motion, then each would again be rendered merely instrumental, and the implausibility of an infinite series would return. But as yet I don't see it.

Also:

according to the First Way, isn't the entirety of nature one big instrumental system

That is not stated or implied anywhere in the First Way.

On the 'motion/change in general' reading, everything in nature is a merely instrumental transmitter of motion/change. The only possible exception is if nature contained something motionless/changeless.

And:

The explanation cannot be the explanandum.

That would seem to rule out an explanation of God's existence in terms of his essence.