Hihi! I guess I'll put in my two cents.
I've healed Levi for a bit now and I don't have mp issues per se. As a WHM I'm always pretty careless with my mp but Levi is a pretty easy fight to heal in general. I mostly spam regent and ss on ot and heal everyone else with med for tidal roars. For his huge aoe I cast a quick c3.
This leaves me not hurting for much mp as I'm doing little but efficient healing. It helps to always have a bard because during the water spume phase it can get a little challenging but I cast med 2 while our scholar casts sacred soil and again it's smooth sailing. Perhaps just try to limit the amount you heal and look for more efficient ways rather then just spamming to top everyone off? I guess I'd have to see you to say. Sorry if my suggestion didn't help.