I guess I owe you a beer or two!
Sure, just toss them over the atlantic!
I just hope the players will enjoy it and not feel like they were railroaded. The thing that makes the adventure is the toy store scenario, and if the PCs aren't "captured" then the adventure would seem a bit bland. They don't have to be captured, but if I can make that happen without it being an obvious railroad, I think the players will have a blast. Unfortunately a lot of published adventures rely on railroading like this; I've pulled it off before, I'm sure I can do it again without it being annoying. This adventure will be a very interesting way to start the new campaign.
If you have any tips or advice from your experience with this adventure, let me know.
I've played this twice. First as a player and then as a DM. Both times it was great! I didn't feel like i was railroaded as a player (guess the DM did a good job!), and my players didn't feel like they were railroaded when i DMed it neither! (I'm just "very good" that's all

).
On a more serious note, what worked fine both times was that player's didn't really feel the threat until it was too late.
That's not to say that you should keep the player's blindfolded until the puppets strike, but you should keep the threat obscure
and somewhat "semi-dangerous" until the events take a decisive turn.
You should make it feel like the player's had all the tips and info required to draw the necessary conclusions, yet somehow, they "missed" combining what was necessary.
The reaction you should go for is this: "Damn! I knew something was amiss! Why are we so stupid?"
Perhaps this doesn't sound any less railroady, but like you said, the fun of this adventure comes from making them play as puppets.
Don't force it on the player's, just make it REALLY hard to be avoided. Perhaps, not all players get captured. Perhaps one or two can escape and help some other way. They'll be outnumbered and will face major difficulties as well.
I understand how my advice is not very story-specific, and perhaps not really helpful, but it's been so many years I've played this adventure, that I don't remember the specifics. What I do remember is the general feel of the story, and how it was a great experience.
I'm running it in the Planescape setting. I'm thinking about using the World Serpent Inn for the first time to get all of the PCs together in Odiare. Then I can make Odiare slide over into a demiplane and keep the Ravenloft fluff working that way. Then I can use the World Serpent Inn to get them to Sigil or wherever I decide they should go for the next adventure.
Irrelevant:
I would give anything to play Planescape again...