This GM would allow an arcanist to lose a prepared spell of the same or lower level of the spell picked for the feat Greater Spell Specialization so as to cast the spell picked for the feat Greater Spell Specialization.
First, the arcanist has devoted the feats Spell Focus, Spell Specialization, and Greater Spell Specialization to perform this trick. And if the arcanist wants to do the same with a second spell, he's to take at least the feats Spell Specialization and Greater Spell Specialization again. Second, the arcanist is dispensing with his most valuable daily resource—his spells prepared—to cast a few more iterations of a spell he probably already prepared. Combined, this is a lot of resources for a few extra spells.
This GM can imagine this possibly being abusive at very high levels—even level 20 casters still frequently cast 5th-level spells (fabricate, polymorph, shadow evocation, teleport, wall of stone), for instance—, but, in the abstract, the difference between being able to cast a spell six times per day and twelve or twenty times a day, while interesting, usually isn't, in the abstract, that big of a deal. With that in mind, I'd argue that for most arcanists this would be suboptimal option: the class already has sufficient spells prepared and spells per day and mechanical benefits to be pretty much the most powerful Pathfinder tier 1 class; throwing 3 feats at doing this seems like a net loss.
Finally, as the question mentions, this ambiguity is likely an unintended consequence of the mechanics introduced by the arcanist class that was published 3 years after the the feat Greater Spell Specialization, and it's not at all clear that this interaction should work this way. This player can imagine a GM ruling that, in that GM's campaign, this interaction of class features and feats totally doesn't work that way, and were I a player of an arcanist PC in such a GM's campaign, I wouldn't argue against that ruling much less leave the campaign over it.