Prince Charon
Just zis guy, you know?
I find myself thinking that by the time they do get back to Federation space, the USS Diana will be unrecognisable as a Hermes-class vessel.
The physics of your setting can very easily restrict you to only one type of FTL.
Iconian Gateways do require subspace; they are stated to work on the same basic principles as Transporters, only inconceivably advanced, and Transporters use subspace.The Iconians have intergalactic range instantaneous teleportation that doesn't require subspace. And lots of Omega Particles....