Found this a bit late, but here's a ship list of new classes I've gleaned from the first four books:
The Sundered
O'Neil Colonies
Neyel Warships
Tholian ships (probably just use the ones from KA/GAW)
Serpents Among the Ruins
Romulan Ivarix-class (The Tomed is of this class)
Federation U.S.S. Universe
Federation Oddysseus-class
The Art of the Impossible
Cardassian Akril-class
Klingon Birok-class strike cruiser (a modification of the Kleev XCA from OP?)
Romulan Amarcan-class Warbird (mentioned in passing in TAotI, but named in Vulcan's Heart)
Klingon Vakk-class cruiser
Well of Souls
Cardassian scout
Vulcan warp-shuttle (Named the T'Pol, big enough to carry its own pod)