I know channeling spells is a heroic action, but are channeled spells resolved during the heroic move portion of the turn? What if my caster wants to move before he casts a spell? Or do you spend the might and then resolve it during the regular move phase? Can someone spell out the sequence of events for casting channeled spells?

You call the channel in the heroic phase and what spell you are channelling and then the spell is cast like normal during the normal move phase.

So you spend the might at the start of the move phase (during the heroic step) and then cast/resolve the spell during the regular move phase.

Yep. Its just like how heroic marching doesn't override priority or movement sequence.

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"Draw your sword with a heavy heart, but swing it with a heavy hand"

No, but once you've participated in a heroic march you cant move a second time. I thought maybe chaneling allowed you to resolve your spell during heroics or something. Glad we could clarify this for me.