It's tricky because you are instructed not to submit anything extra, and giving general advice is almost impossible in this case. My recommendation would depend on your specific situation, keeping in mind that there is actually not much you can do to influence the adcom at this stage. Their decision to interview you will largely depend on the pool of applications they get in round 2... Yet, I would not completely sit still if I were in this situation.
First, you should receive an email from Dana Scalisi (assistant director of admissions) soon. I would simply reply to it, and reiterate my interest and motivation to join the HBS community. Keep it short.
Then I would follow instructions by the letter as much as possible.
If you haven't gotten a chance to visit campus already, do so (if you happen to be around Boston or have always wanted to visit the town, which is actually very nice). Take a tour of campus, attend a class and an info session if you can. It's subtle, but it clearly won't hurt your chances, and come interview time you'll be better prepared to explain why HBS is the right program for you. You may want to inform your admissions officer of your upcoming visit, but be mindful of their time and do not insist on meeting them.
Have you been encouraged to apply by a Harvard community member? Let them know about your situation, and if they are a very strong supporter they may feel compelled to intercede in your favor. It cannot hurt your chances if it's sincere and from someone who truly knows you well. Never ask for such a favor however, it has to be that person's own initiative, and it would be inappropriate to ask for it.
Finally,if anything major occurs at work (e.g. an unexpected and significant promotion), and only in such a case, I would try to let the adcom know. Do NOT write another essay. Just be factual and send them a brief email explaining the situation with the hope that they'll consider it. There is no guarantee, and you have to apply judgment. But if the change in your situation is truly substantial, I think it is worth giving it a try. Do not send an email or contact the adcom to inform them that you beat your sales target a whole month before year end...
I hope this is helpful. If you have any comments or suggestions, I'd love to hear from you, as this is a rather unusual situation.
The difficult thing here is that you are not officially on the HBS waitlist. You are just back to where you stood a couple of weeks ago when you submitted your application.