When was the first drawing of the Phoenix ever shown? Was it in a TOS episode, or in a book or something?
I mean before the John Eaves design
Regarding inertial dampener fields. I don't know why you'd need them honestly.
If you used an Alcubierre drive system, which at least one scientist working on TMP suggested more or less the same mechanism (though years before Miguel Alcubierre actually drew it up)
there would be no feeling of acceleration as a result of warp-drive.