Sounds pretty much spot-on; especially the trained militia part.
Clearly I need to give Campaigns a closer read than I have, I've mostly been looking to Battles. One of the things I was noting was form, that troops who haven't actually trained together might be one class down from the standard. So Irregular>Loose>Formed is the progression and training would sort that out.
You definitely should give Campaigns a close look. It has a lot of material that will address what you're worried about here.
Also worth noting - don't let the presumptive sizes of the forces fool you. They can be much higher.
The Vassal Troops by Realm Size table assumes garrison expenditures of 2gp per peasant family each month. Borderlands and wilderness domains may have more troops, as may highly militarized societies. A realm engaged in “total war,” such as Germany during the 30 Years War, or Rome during the Punic Wars, might have a garrison 50-100% larger than listed.
In terms of ACKS rules, this simply divides the number of peasant families by 3 to reach the same demographic figures. That still leaves a pretty massive state, one which would have no difficulty finding 180 people to train 9,000 men. I’m simply pointing out that your complaint that it takes too many men to train a phalanx is off-base because you aren’t considering the scope of the nation-states that were fielding phalanx. I will concede that the ACKS figures of 3 soldiers/10 families (conscripts + militia) is historically way low. Able-bodied men capable of military service form approximately 1/4 of historic populations, but usually a sizable portion of that was already in military service or wasn’t legally compelled to provide service (service was required of citizens /landowners depending on the particular time period, not slaves).
Now, as for how Macedon raised such an army historically (or the Romans for that matter), it really is as simple as the last paragraph that James quoted here. Ancient (and medieval) nations had an extensive organization dedicated to training citizens to fight when necessary. De Re Militari, which I mentioned in my previous post, outlines exactly how that was done in the Roman Empire. Hellenistic Greek city states operated on a very similar basis, with citizens being trained to fight when they were young men and being required to provide military service on an as-needed basis (rather than serving as full-time soldiers). When Macedon and Rome were calling up thousands of people to build a “new” army, they weren’t starting with raw recruits. Even so, both of those nations fit the demographics that I cited in my previous post as well.
tl;dr: any state big enough to field thousands of troops is big enough to find 100s of people to train them.
As far as training people who “can already fight,” I’d argue that you’d actually need MORE trainers, as learning how to fight as an individual is minimally applicable to fighting in a Phalanx and the aristocrats you described in your original post aren’t going to listen to some punk adventurers and are going to need to overcome a lot of bad habits (like moving around while they fight, for instance).