Iridium appears to be using a vocoder called AMBE. Its quality is similar to the one of the MELP codec from the demo and it also runs at 2.4 kb/s. LPCNet at 1.6 is a significant improvement over that -- if you can afford the complexity of course (at least it'll work on a phone now).
Based on my previous experience with Iridium I believe it actually operates at a data rate up to about 3 to 3.2 kb/s. 2400 bps of it is actual usable voice payload, the remaining 600 bps is FEC.
Iridium data (not the new next-generation network) service is around the same speed, it's 2400 bps + whatever compression v42bis can gain you. For plain text and stuff it can be a bit faster, something that's already incompressible by v42bis will be right around 2400 baud.
