Raid events are not rerun. Your only chance to get Reiki is now.

However, starting from July, you'll be able to exchange unneeded SSRs for past raid Eidolons. 4 event SSRs per each. So if you need 4 more copies, then that's 16 event SSRs you'll need to exchange in. There's... 8 Union events until then, so if you are in a decent Union, you're going to get 32 absolutely useless event SSRs by then. With zero effort on your own part. 40 if you manage to hit the personal PP cap in each one.