That doesn't describe the games I run.
There is a reason for that. I'm not at all sure that you are actually describing sandbox play. Instead, I think you are confusing an attribute of gaming usually associated with sandbox play, noting that your game has that attribute in spades, and drawing the conclusion, "I must be running a sandbox."
I'm not sure that conclusion is warranted. What you describe doesn't fit any classic definition of sandbox. It might be a Sandbox, but it seems to me that it has features not associated with sandbox play in general, so I think its up to you to prove that your game fits in the definition commonly understood for sandbox. Otherwise, it's just 'sandbox as I use the term'.
Naturally, maybe its my understanding of how the term is commonly meant that is in error, but we'll see.
Ive written up an outline prep in the OP. I can't see how it fits your definition and, in fact, I've never, ever run a sandbox game according to that definition.
Well, yes, that was one of my points.
Here's the thing; you seem to be describing a game which features alot of player empowerment. Player empowerment is usually associated with sandboxes, and usually not associated with adventure paths - especially by the sort of people prone to calling adventure paths badwrongfun. However, the question becomes, when we speak of 'Sandboxes' are we talking about 'player empowerment' as its most salient feature, or are we talking about non-linearity as its most salient feature.
Elsewhere, I've talked about how 'Railroads' are distinguished by linearity alone but by linearity plus low play empowerment. I've also suggested that we can't say that Sandboxes necessarily feature high player empowerment, using the term 'Rowboat' to describe this situation. You've described a collaborative world which is almost the definition of high player empowerment, but the fact that the world is collaborative and thus player empowering doesn't necessarily make it a sandbox. Personally, I think that you are describing something that resembles an 'Adventure Path' but with a very (very, very) high degree of player empowerment. The game is linear in a sense, but rather than having one person setting the agenda, you are having a group set the agenda and doing much of the preperation collaboratively.
While there is some sort of exploration going on, it's not exploration in the usual sense because with a collaboratively created world the usual sort of discovery - the players encounter something that they previously didn't know about - is taking something of a backseat in your game to other considerations.
Frankly, I don't think you are engaging primarily in Simulation/Exploration and the other priorities associated with Sandboxing. I think you have a game that is pretty strongly in the Narrative/Story corner of the triangle. Now, I resist that description because I disagree with some core tenents of GNS (to say nothing of the fact that hitherto in this post I've used a square rather than triangular geography mapping games), but nonetheless for the purposes of this discussion, I think that's additional evidence you aren't in a Sandbox, but rather in a Theater. The fact that your game set up and preperation resembles a traditional theater game more strongly than the game preperation normally associated with classic role-play games - and high simulation games in particular - is to my mind yet more evidence.
The prep required for my sandbox games is decided by the decisions facing the players. The hypothetical fact they have unlimited choices doesn't really matter - it certainly doesn't need prepping for. The flow of prep follows the decisions being made by the players. See my post above for how I'm using the terms choice and decision.
There are practical constraints to anyone's game that make talking about games in terms of absolutes difficult, and sometimes unhelpful. Nevertheless, I agree with you that in your game, "The hypothetical fact they have unlimited
choices doesn't really matter - it certainly doesn't need prepping for." That is I think, with a slightly different emphasis, precisely my point. Your players are actually making some of their most relevant choices before entering a scene frame, and indeed making these choices at a metagame rather than in game level. That certainly doesn't sound like a sandbox to me, which is normally associated with continuous framing, GMs as nearly pure referees, and a high degree of simulation. You have players in the Director Stance, which is strongly associated with Nar play and not Sim play. Again, while I'm not sure there is a 100% correlation between the terms 'Sandbox' and 'Simulation', and I'm not even sure 'Sandbox' is formally defined anywhere, there is to me quite a bit of overlap between how I understand the communities that use the term are using them.
Don't mix up the metaphor - "a sandbox" - with the thing the term was coined to described.