You did answer your own question, and the most succinct description we came up with on the board for phased combat is:

1. winners of initiative perform their Phase 1 actions
2. losers of initiative perform their Phase 1 actions
3. winners of initiative perform their Phase 2 actions
4. losers of initiative perform their Phase 2 actions

Technically, combat movement is simultaneous; we clarified this point in the Second Edition Players’ Manual. Assuming both the fighter and the orc have MV 30, then they each would move 15 feet during phase one; the fighter would end up where the orc started, and the orc would end up at the door. In phase two, the fighter would continue his movement to the door and (based on the fighter’s winning initiative) attack the orc before the orc opened the door.

rhialto wrote:

Hmmm, guess I need to revisit the rules...so, RAW, is the orc trying to open the door in front of him not considered a "movement", and so not considered "simultaneous" as the fighter moves 15' towards the orc opening the door? With such few categories of Combat Actions I think I'd classify the "open door" as a movement...

I think I'd rule:
If "movement" is simultaneous, then the orc has a chance* to move 15' and open the door before the fighter can move 30' and attack, even though the fighter won initiative.

*And this is where I'd invoke the Non-Standard Task Resolution of x in 6 chance, or maybe a Saving Throw; probably by having the player of the fighter roll to see if he gets to the orc before the door is opened.

And here I thought the succinct 4-bullet point answer was the EABA...
 

See VOL. III, p. 240: COMBAT, other potential actions. Melee, missiles, magic, and movement are not quite all encompassing (though we tried). Players will propose actions that don’t fit firmly in any of those buckets, and the referee will need to rule case by case.

It's situations like these that probably had me removing "simultaneous movement regardless of initiative results" from the 2E hardback. I recall that during the Players' Manual development, David thought it was a feature that we should not have lost, as it was part of the 1e boxed set, and I wasn't in disagreement. 

The spirit of the rule, as I had originally intended, was this: When two combatants whose intended actions are to move and engage one another, they meet at about middle of their respective starting points (based on their respective movement rates). It's a fine rule for adjudicating those situations, because each combatant advances and the initiative winner attacks first, typically speaking.  

But then we have situations as illustrated above. If movement is simultaneous regardless of initiative results, it begs the question: When is an initiative winner not an initiative winner? Why, when there is movement involved, of course! So, there are situations where I am not overly fond of the rule, and it brings me back to why I probably phased it out from the 2E hardback, because after ten years playing this game, I've seen so many situations where it makes perfect sense, and other situations where it's problematic. 

During the initial development of the game (2008–2011), I was trying to achieve a system of combat resolution that did not give the impression of pawns taking turns moving in a chess match. In those years I was really tired of 3E combat on grids, and all these combatants paused on the grid, waiting for others to take their turns. In AS&SH, I think that we do achieve superior flow with phased combat, and sometimes with the implementation of simultaneous movement, but I can see that situations like the fleeing orc and pursuing fighter can have less than ideal results.

These days I'm more inclined to ignore simultaneous movement, unless it pertains specifically to two enemies advancing towards one another with intention to engage. I want that fighter to move half and cut down that orc; and I'd want the orc to be able to do the same, if the shoe were on the other foot. Of course, you are the master of your own game, and all rules are guidelines for you to use as you see fit. AS&SH is still evolving and refining, even after a decade. Do what thou wilt, my friends!

Ghul wrote:

In AS&SH, I think that we do achieve superior flow with phased combat...I want that fighter to move half and cut down that orc; and I'd want the orc to be able to do the same, if the shoe were on the other foot.

To me this is the charming simplicity of the phased combat, and the succinct 4 bullet-points: consistently applied, they keep combat moving along.