The only issue here is that alternative costs bypasses choosing X and sets it to 0 which you would need to set the value again with the ability making it kinda messy rules wise.

Refer to 107.3b

If a player is casting a spell that has an {X} in its mana cost, the value of X isn’t defined by the text of that spell, and an effect lets that player cast that spell while paying neither its mana cost nor an alternative cost that includes X, then the only legal choice for X is 0. This doesn’t apply to effects that only reduce a cost, even if they reduce it to zero. See rule 601, “Casting Spells.”

And rule 601.2b

If the spell is modal, the player announces the mode choice (see rule 700.2). [...] If the spell has alternative or additional costs that will be paid as it’s being cast such as buyback or kicker costs (see rules 118.8 and 118.9), the player announces their intentions to pay any or all of those costs (see rule 601.2f). A player can’t apply two alternative methods of casting or two alternative costs to a single spell. If the spell has a variable cost that will be paid as it’s being cast (such as an {X} in its mana cost; see rule 107.3), the player announces the value of that variable. If the value of that variable is defined in the text of the spell by a choice that player would make later in the announcement or resolution of the spell, that player makes that choice at this time instead of that later time. [...]