In that scenario, I would choose the fully break limited weapon over the 3/4 eidolon. Reason being that Ixion isn't particularly good if you don't ever plan to use a thunder party. Her battle buff increases thunder damage, which is near useless for every other team. Unless you're using a eidolon that she can replace by a notable difference in hp/atk, going the weapon would be better in the long run as long as you plan to level up a thunder team, even if just on the side. Going Ixion would be better in short term but she'll most likely be replaced much faster in anything outside of a thunder party as she most likely won't provide any use.
If you were still a new player then I would have suggested the eidolon but seeing as how you can gather enough materials for that much, I would assume you can already handle expert and possibly ultimate.