"Another notable document is a letter from Hittite generals in western Anatolia appealing to the king for reinforcements in men, horses and chariots to fend off enemy forces. "
I had assumed they had to wait for clay to dry before it could be carried anywhere, which seems incompatible with using them for urgent military messages. I wonder if there was a way to transport them while soft, or if this was just the archival copy of a message sent by other means.
It's not like they had to wait for the clay to dry, and then sent the message via email over fiber optic cable. It would take days to reach the palace. Drying it (maybe in a small kiln?) first was a small part of the delay.
Most tablets were air dried, which would take a day or two. But some tablets were fired - dried in a kiln. I don't know about Hittites but at least in Mesopotamia, air drying was by far the most common method and only some important ones were fired. So methods were certainly available to dry a tablet quickly if necessary but I doubt if air drying delays made much of a difference. Messages and goods were limited to the speed of horse after all.