It's hard to speak to the applicants you've seen who've started a new job in Sept & then joined HBS the following Aug but in all of my years of experience working with MBA applicants I feel confident in telling you that starting a new job at a new company right before you apply to b-school can be a red flag.
Put yourself in both the adcom's shoes: they know that it's extremely unlikely that a hiring manager at a new company (outside your current co I mean) will hire you knowing you plan to leave in a year. The exception is if you plan to return to that company following graduation - then you'll come back with the skills you gained in b-school, ready to make an even bigger impact. So, the adcom's concern will typically be that you were not honest with the new hiring manager/new company, which then raises red flags about your integrity. Generally speaking it takes about a year at a new company before they really start to see a ROI on you.
On the flip side, the adcom will also worry that if you just took a new job you may not be serious about b-school. I think the 1st issue (worrying that you were not honest with the hiring manager) is generally the bigger concern though. And since it's generally impossible to get an LOR from that new manager it's hard to refute that concern.
Like I said, there are some exceptions: saying your post-MBA goal is to return to that company (which it sounds like is not an option in your case given what you mentioned about your goals) or potentially taking some sort of contract position that has a definite end (which can be hard to find), although generally speaking the adcom prefers applicants in full time, permanent positions.
Aside from these challenges there's just the reality of the fact that if you take a new job in you're not going to be able to say anything about it in an essay or an interview (as you point out - and I totally agree), so the adcom will just be taking your word for it that it "will" make a positive contribution to your overall candidacy, but the truth is that's sort of a leap of faith since you most likely will be too new to have DONE anything yet.
I do think that if you at least make a move within your current company you can get up to speed more quickly & it also just shows more continuity - and then the integrity thing is more of a non-issue. You've already put in your time at this company & shown them a return, so making an internal move is not going to be seen as a decision lacking in integrity. To put it bluntly, you won't seem as if you're screwing your company over the way you might if you take a new job at a new company with a plan to leave in a year. And since it's an internal move there's more chance you can have an impact more quickly (since you don't need as much time to get up to speed) & could possibly have something to speak to at least in an interview if not in an essay. I think your strongest move would be to get that internal transfer.
In your case I think the Wharton admit is part of what makes this tricky. You can certainly reapply to HBS & see if the new international experience helps differentiate you but of course there's no guarantee & it would mean walking away from Wharton. It sounds like you will have a good shot at other top 5-10 schools since you got the Wharton admit & the HBS WL but of course there are no guarantees there either. An important factor will also be how many years of work experience you have already. If you're already at the top of the average that will make it more difficult to reapply.
Have you already sent updates to HBS? A new LOR can help as can any updates on any new accomplishments you've had since you applied. How was your GMAT score? Increasing that could help as well - both because a higher score is always better & also because it shows that you are serious & doing everything you can to improve your candidacy. I'd recommend another visit (or a first visit) to HBS as well again to show your continued commitment.
Hope that helps! Unfortunately there's no black & white answer here & it's a bit hard to speak to all of this in theory without having seen your original application, but hopefully these pointers will be helpful! Good luck to you!