Hm.
Hm.
Well, off the top of my head, I can think of three things that could be done right now.
1. Nothing. It's something that's nice to know, but we're pushing it being here in the first place. Certainly the safe option. It's also really boring and potentially a waste of a once-in-a-lifetime opportunity.
2. The "Fuck You" option. If possible, leave a time-delay or remote-triggered program to inject a video message of defiance and revolution straight into the Emperor's cerebral cortex, followed up as much white noise will fit (I can't imagine having random noise shot straight into your brain does good things). Even better, code it to go resident in the Emperor's mind, jump around in his brain to avoid detection and run on a loop. You want to leave an impression? I think this will do nicely. The real question is if this is even possible and do we want to so thoroughly burn out bridges on this one. Still, if we're going with balls-out war, this would be the cherry on top of one hell of an opening salvo.
3. The "diplomatic backdoor" option. Similar to option #2, but instead of just carpet bombing his brain with our message and then giving him the mother of all grand mal seizures, we leave a message that if he's willing to listen to us and work towards avoiding what will certainly be a lengthy and costly war between Earth and the Imperium, we will be keeping a covert method of virtual contact open, exclusively for the Emperor himself, without interference from the military. This would be set on a longer timer, like maybe a day or so after the Napai raid. This takes advantage of the fact that we essentially stumbled upon a private hotline straight to the Emperor, and that we can possibly convince him to agree with our cause, and that the guy's even real and isn't some AI construct.
The third option is by far the most risky, as it is predicated on the idea that since we've seen practically nothing of the Emperor himself anywhere, not even as a talking head on some holoprojection, the Imperium is very much like Imperial Japan in WW2, with the Emperor still nominally in charge of the government and its figurehead, but with the real power currently vested in the military leadership (and that the guy's even real). If the Emperor ever wishes to consider our demands (cessation of attacks against Earth and the introduction of a Magna Carta of sorts for the Imperium and the transfer of power to a more democratic republic or parliamentary format, or at the very least recognition of Earth and her allies as a legitimate government and allowing all planets the option of joining either side at will and democratically), we will be listening. I know that this is a long shot on a completely uncertain factor (we have no clue if he really is like Emperor Hirohito or is just a raging psychopath who wants us all dead). I am also aware that all the historical precedents I'm citing here (Japanese at the end of WW2, the Magna Carta) happened after the side receiving the demands had their asses handed to them. Still, a quick and diplomatic victory is preferable to any other in this case, and even if he does nothing but taunt us initially, possibly after a few major defections and defeats, he might be willing to consider our terms. Hopefully we can make it clear that there are no winners if we fight this war, and that a more peaceful transfer of power is in his best interest and the best interests of his people.
Then we'd just need to take out the Imperial military after they appoint a new Emperor, declare war on the guy who sided with us and become even more crazy and hardline than before. Because, you know, that would be the easy part.