I'd say adding time mage is a terrible idea.

Time mage is definitely a support/enfeebling type of job

With that said the pillars of Time mage would be the same as Red mage and that's with slow and haste unfortantly for RDM if you take slow away from RDM thats really it for RDM and all that would be left is para for a job that is ment to specialism in enfeebling.

Anyway, I kinda feel that RDM is Time mage any way with chainspell, slow, fast cast and haste, being the main traits of what time mage really is.

Personally, I'd prefer a Time mage gear set for Red mage more than then adding a job that would probably step on the toes of some many others.

With that said some of your ideas would be great for RDM

Old, Reflect, Stop and Mute would be things that would breath new life into RDM.