Quantum Slipstream always struck me as a probable "re-branding" of Transwarp in light of previous failures associated with the term, just like "transphasic" seemed to replace "interphasic" tech after that unfortunate business with the Pegasus.
It seems transwarp is more deflector than drive on the face of things. That little transwarp coil our Voyager heroes boosted from the Borg didn't seem like an engine or drive core component. Perhaps it helped deflectors punch transwarp conduits open.
Relative to previous ships, the most distinguishing feature of the transwarp prototype USS Excelsior was the increased hull volume around the deflector dish, suggesting some possible new gear associated with the dish. Similarly, the NX-01A Dauntless had a unique grille type deflector in place of the usual dish mechanism.
Incidentally, the "warp 13" references in TNG:AGT could be verbal shorthand for an era where speeds of "warp 9.9995", etc., might be common and a slight nuisance to spit out. Just superimposing the sub-warp 9 scale over the warp 9+ equivalents seems to make sense.