I don't like commenting here because I know it's gonna be removed because of time, but I got thoughts and this is the only way I can communicate without making more damned accounts.
I think the other core shards are with Hakari and Sukemaru. Hakari doesn't trust humans, and the majiks they've surrounded themselves with (all 2 of them) are also human-haters. If I were Hakari, I wouldn't trust burying my core behind some vault or in some random corner, just on the off-chance that there's a spell that makes getting that easy. It'd be better to trust my core shards with other majiks whom I could trust. It also makes sense for Hakari to trust their own power, as stealing their magic core shard away from them should be damn near impossible. Sukemaru, though they're small and weak, are very firmly in Hakari's camp and with being invisible, are very hard to find if you don't know they exist. And Mayoi's portal powers should mean that chasing them to capture it should be impossible.
That said, I think Mayoi is a very creative person, and wishes they could share their creations with the world. Hakari's palace is excessive and extravagent, and that card game would be a lot of work to make. Their creative pride is a potent flaw, and I think their trial might involve exploiting that.
Also, surprised Sukemaru's trial isn't to just capture them. Maybe it's to avoid them in a game of tag?