Although the rules don't mention it, letting go of a two-handed weapon with one hand or putting a free hand back on the weapon is a free action for you.
As a side note, Mobile Spellcasting allows you to cast a spell and move as a standard action. Arcane Chanelling allows you to use a standard action to cast a spell and deliver it through a weapon with a melee attack. Those are both different things and both require a standard action to activate. I do not believe these can be used together as advertised by BowStreetRunner.
Somatic Weaponry might be a better option, as it does not cost a higher spell slot.