APM: A few words behind the philosophy of engagement and overrun. ACKS attempts to encourage formation fighting and combined arms. For example, in ACKS its a very viable tactic to have a front row of heavily-armored sword-and-shield, a second row of lightly-armored spear, and a third row of spellcasters. The rules are structured such that it's hard to get to the spellcasters. Because any hit will interrupt spellcasting, it means that mages need warriors to protect them if they're to be valuable in battle.
ACKS: I know that 3.5 had similar design goals, but I felt it's approach was sub-par. The AoO mechanic was a very slow and tedious means of creating zones of control. Moreover, tumbling was far too easy for characters past mid-level who cared about the skill at all. In ACKS we reverted to a true zone of control system (the 5' engagement system) inspired by old wargame-style mechanics. Overrun then becomes necessary as a technique to overcome the zone of control. I wanted a system that allowed, e.g., a high HD creature to be more effective at exerting a zone of control than a low HD creature, and basing it on saving throws proved a good choice.
If I understand correctly, the only significant limitation to Overrun is that you can't move (other than Defensive movement) when engaged (so Overrun is right out).
APM: That's not actually correct. An Overrun is a special maneuver, not a movement. You can begin engaged and attempt an overrun. If you succeed, you can start moving past the creature that was engaging you. If more than one creature was engaging you, though, you'd have to overrun them all.
Similarly, because you cannot move after attacking, an engaged character cannot drop the opponent engaging them and then Overrun one or more opponents more than 5' away.
APM: That is correct.
However, if a character begins unengaged, and is lucky, they can Overrun through a wall of opponents to the full extent of their movement, correct?
APM: You'd have to be quite lucky...As others have pointed out, each opponent can make a saving throw to attempt to block the character.
In the case of simultaneous initiative, an opponent is moving to engage a currently unengaged character -- that character could Overrun the opponent to avoid engagement, correct?
Is a character engaged if they are 10' away from a wielder of a second-rank weapon?
Do you know of a good defense against Overruns?
APM: A scrum of 3-4 defenders, one of whom is statistically likely to either not be hit, or to make his saving throw, usually does the trick.