Spot on, Kingreaper.
That's exactly what I'd do for the situation where two parties seem to be in harmony but somebody wants to begin combat: for example, the classic, "on my signal, everybody at the banquet table draws their swords and attacks" betrayal, or the classic "we sign the peace treaty, then as the other side drops their guard, we attack" back-stab.
For the situation Ferghis described, though, I don't think there's any chance of Surprise in that situation, by RAW. Since both sides are aware of each other and ready for hostile action, there is no Surprise round. Simply roll for normal Initiative when somebody declares "I open fire."
This is pretty much the equivalent of the classic "Gunslinger" scene: it doesn't matter which one of them says "I draw and fire!" first at the tabletop, it matters who rolls a higher initiative. The winner gets the drop.
Tying that back to our "Total Defense" example, think of it like this: the front-liner who wins initiative gets to enter Total Defense if he wants to, and thus be in Total Defense when the archer actually lets fly .. (or, if you prefer, by the time the arrow arrives - arrows, unlike bullets, have visible flight time.) The front-liner who lost initiative had had his concentration wander for a moment, was looking at the wrong archer, blinked, coughed, whatever, just enough that he wasn't in the benefit of Total Defense at the moment the battle started.
And getting all the way back to our "Busting through the door" example, where the crossbowman has tried to ready an action on "seeing a target on the other side of the door", Initiative determines how quickly he is able to spot the target, recognize it as a hostile / not-hostage, aim at it, and fire.
Likewise, Initiative determines how quickly our door-opening fighter is able to go from shouldering the door open back into his fighting crouch with shield and sword interposed between himself and the room.
Whether they're in a Surprise round, or a normal round.
. . . .
I think you can sum up my position by stating it thus:
When multiple creatures are ready for combat to break out, Initiative is the RAW means of determining which one reacts to the trigger that starts combat most quickly.
I think any other interpretation winds up with a bunch of Initiative-number-collisions, e.g., in my archers-ambushing example, would all of the archers act on the same initiative because the trigger that started the combat occurred at the same instant for each of them? That just seems .. ridiculous .. to me.