I think you probably can - but the question really comes down to does the Amulet of Mighty Fists count as a melee weapon?
The answer is yes.
The amulet of mighty fists states
"Alternatively, this amulet can grant melee weapon special abilities, so long as they can be applied to unarmed attacks."
and spell storing is part of the melee weapon special abilities.
so it's pretty cut and dry.
I agree. However given the cost (even with the new changes) and the +5 cap on total enhancement + abilities, it's probably cheaper and just as effective to carry around a spell-storing monk weapon.
since it would be 4,000gp for Amulet of Spell Storing Mighty Fists, or 8,300 + Ngp for a +1 spell storing N,...
It might not be worth it at higher levels, but out the gate, its cheaper to have the spell storing mighty fists. You're paying money for double weapon enhancement. You wouldn't get one spell stored in each fist though, you'd just get one in the amulet.
Yup the amulet of mighty fists is relatively cheap for a single enhancement but costly for two or more (but still useful if you want to stack effects over having bonuses)
Spell storing may and likely is less dpr than other enhancements but the flexibility and action economy (and nova potential) is quite intriguing.