The reason why [Pure Energy] cannot be converted into [GPE] is because [GPE] is Pure Energy with genetic data of its owner. Like a character-bind weapon in MMORPG that cannot be worn by other player. You simply cannot register your genetic data to a [Pure Energy], it won't work the same as natural [GPE] and an Esper won't able to use that energy because it's not coming from their body. It's genetic. 

There is a cheat in this case actually, convert [Pure Energy] into... a pill or something and take it. And like any typical medical experiment story would, will have a side-effect of whatever it is.

On side note, I like your idea of having her as a glutton. *Imagining a scene where a loli helplessly want to eat all day long*