It's occurred to me that we shouldn't pick C:
You remain at the center of things on your throne, gathering information and directing the war effort. Your immortal and Gieloth allies should be able to handle the frontlines without your intervention.
Another group of scholars have come up with the idea of establishing towers for signalling along the paths of the empire. You recall that Astarth once threatened you with such an idea. With a tower, an oil lamp, a mirror and a book of codes, it is possible for messages to be transmitted long distances at a speed faster than land travel.
In this update, we chose to build a road network. That means a much faster flow of goods and people, but the flow of information is still significantly slower than if we chose to build signal towers. It will take way too long for information from Greece/Anatolia to get back to us so that we can respond accordingly. By the time we've received the information, the situation will have already been resolved. Therefore, we have to commit to a course of action.
Athena is backed up by 10,000 men thanks to our road network and she's probably the best general we've got. She's probably quite happy that we've sent more men to bolster her forces, but if we try to come to Greece on our own, I believe it'll be seen as meddling. We've already sent reinforcements, that'll be more than adequate.
As ScubaV said, Edem and Sekhenun aren't really adept at tactics, so our presence with the invasion force just makes more sense. Supervising the invasion so that we can dictate terms to the Hittites is necessary, plus I want to ensure a swift victory to ensure minimal casualties on both sides. We need all the bodies we can get to monitor the Terasphagos threat.
The Emperor's presence will be needed in Anatolia to make sure our men behave themselves:
Valli - Assurdan's right hand man and a skilful warrior. Dislikes Gutians as they destroyed his village. Dislikes Hittites as they killed his father. Dislikes Babylonians as they killed his grandfather.
I don't want a loose cannon like Valli pillaging and slaughtering people at Hattusa once we've conquered it. I want this invasion to go as smoothly as possible and with minimal collateral damage. That way, the Hittites will be less likely to revolt against us.
Edit: A few random thoughts:
Super-Soldiers
I wouldn't recommend going the super-soldier route, largely because we opted for a spy network instead. We don't have a base of elite troops from which to draw from. Unless we can create Watchers with invisibility powers, I don't think it's a good idea. Let's see what other research opportunities Sekhenun has on the table.
The best countermeasures we've had thus far against the current Terasphagos strains have been a result of fortifications and numerical superiority. I believe that our focus should be on (1) increasing the size of our army by vassalizing the Hittites, and (2) advancing the state of our weapons tech so our standard troops have better equipment. It should be easy to issue our men new weaponry after we've invented it because of our road network.
Expedition to China: Logistics
We have two goals here: (1) Get to China as fast as possible and (2) Minimize attrition and avoid fights along the way while doing so. Sending 20,000 men from Babylon is going to be a disaster if only 10,000 remain once we reach China.
Sending an army across the continent is going to be a nightmare, but I believe we've laid the groundwork for it. The first part of our journey will actually be relatively easy; our road network will bring our army together near our borders quickly, and since we've managed to stop the Gutians from raiding us further, we should go through the mountains to avoid the rebellious Indus Valley.
We should also send a few Watchers out east, beyond the mountains into Central Asia. They can keep an eye by infiltrating the local civilizations there, and when our army arrives they'll tell us where we can resupply for food, whether there's any local resistance, etc.
I'm going to offer up the unorthodox suggestion of bringing Akilhotep with us to China. He may not be well-versed in military matters, but he is a superb administrator, and to me, that says that he is a man who will be crucial in helping us with logistics. In fact, Iltani might be even better for this, because she's studied the military tactics we invented:
“I’m great with letters and numbers, and I also know plenty about the uses of plants. Father insisted that I learn as much as I could about civilized ways as I was to be a princess. He also made me study the precepts of some old Akkadian king that was a big influence on Sumerian military tactics.”
She might be even better when it comes to help with logistics because she's more well-versed on these matters because of her father. She could also parley with the Gutian tribes so that we can be assured of safe passage. As much of a pain in the ass she was last chapter, her skill set seems perfect for this.