There's no reason not to use your dualcast while moving. On both Bard and RDM, I've never experienced using an instant causing me to not be able to continue moving. If anything, Contre and Fleche would interrupt your movement for animations, but they don't.

You shouldn't be going in to melee combo without burning your dualcast first.

Maybe it's because I started on Bard and was used to monitoring DoT's, but I have my indicators enlarged and right under my character and I have no issues monitoring DualCast.

I can see how adding it to the Job Gauge will be useful though.