I wanna try to push this debate in a new direction, by focusing more on the identity of the Lady in Red. Watching the first 0:55 seconds of the Stormblood teaser again, I imagined that she may not have been much different from K'lyhia in the Arcanist quest line.
ACN story spoilers, anyone who might be new to FFXIV:
To get closer to Doesmaga, K'lyhia donned a borrowed outfit, which belonged to one of the performers of Costa del Sol. IIRC, she posed as a dancer (not relating to what we see in the SB trailer), or a courtesan of some kind, and even put on an act.
Suppose that the Lady in Red could have been doing just that in Ala Mhigo, while 2.0 thru 3.4 was going on here on our side of the continent. She could very well be a Monk who is witty and tactical like K'lyhia, donning the outfit of a dancer or courtesan to get closer to an enemy.
If she is truly a DNC, in the story or otherwise, I don't think we have to worry about similarities in fighting style. After all, look at the Ninja. Ninjas are typically martial artists, yet the NIN fights nothing like the MNK. I believe SE could pull that off with the DNC.