Is there a way to get the effects of the evocation wizard’s Empowered Evocation on a magic missile at a much lower character level?

At level 2 a Lore Master wizard has the Spell Secrets ability. This allows the wizard to change the damage type of a spell, like magic missile, from force damage to fire damage.

If a character multiclasses into Phoenix Sorcerer she can use her Mantle of Flame ability to add her charisma bonus to one fire damage die roll.

Or a character could multiclass into Dragon Sorcerer and use the Elemental Affinity ability at level 6 to get the same effect on a variety of damage types.

Frozen, flaming or electric magic missiles sound kind of cool. Adding bonus damage sounds powerful.

Do these builds work? Is getting a level 10 ability this early too unbalanced?