I've been thinking ever since I've tried Red Mage that it would be a bit exciting if somewhere down the line that healers also could get a PVE movement ability like most other jobs now have.

[SPOILER]When we spar against Lyse in Stormblood in a cutscene as seen in the opening movie, we move quite fast when jumping forward, even as a WHM, so it's not unwarranted to have movement utility.[/SPOILER]

Some suggestions:

WHM
Surf: Move quickly in the direction you're facing. Water force slows enemies where activated for 1 sec. Range 5 yalms, radius 2.5

AST
Distort: Teleport 5 yalms in the direction you face. Distortion slows enemies for 1 sec. Range 5 yalms, radius 2.5

SCH
Converge tactics: Fairy pulls you to itself in a 15 yalm range.

DNC
Leap: Rushes to target and heals self and nearby ally. Movement speed increased next 2.5 secs.