Can an artificer/wizard make a homonculus heart into a spell-storing item?

The Homonculus Servant infusion requires a specific component:

Item: A gem or crystal worth at least 100 gp

Later, it goes on to say

The item you infuse serves as the creature’s heart, around which the creature’s body instantly forms.

Okay, while gemstones are assumed to be just valuables, what is a crystal? The PHB lists the following forms for an arcane focus:

Arcane Focus: Crystal, Orb, Rod, Staff, Wand

Admittedly, the crystal has a listed cost of 10gp, but it’s reasonable a fancier one could be made to fulfill the requirement.

Moving on, the Artificer’s Spell-Storing Item feature lists as its possible targets

one simple or martial weapon or one item that you can use as a spellcasting focus,

An artificer must use a tool they are proficient with or an item they have infused as a spellcasting focus – this means that a finished homonculus can be turned into a spell-storing item, but it’s rather unclear if it can then touch itself to cast the spells stored within itself.

… but, if you pick up one level of wizard (or the magic initiate: wizard feat, perhaps? Actually, no, that deserves a question of its own), you can use the crystal as a spellcasting focus, since the feature does not specify it must be an artificer focus.

Thus the plan. At the end of a long rest, touch your expensive crystal focus, imbue it with your desired spell, then infuse the focus to be the heart of your homonculus, which it is rather difficult to argue isn’t touching its own heart at all times, letting it cast the spells within the item even by the strictest of RAW readings.

Is there a reason this wouldn’t work?