Well your post was a bit confusing.
You said "those final fights", so I thought you meant the head/body/pants that were rewards from those scenarios. But I just double checked and saw they also drop a KI to let you pull an item from the Tenshodo box.
But those accessories werent random augs either as they had a set pool of augments. Also, I dont think they can put auged stuff in the treasure pool, so it would be another KI conversion.
I'm fed up of random augs though, especially for something like this:
https://ffxiclopedia.fandom.com/wiki/Ebon_Key
I dont entirely trust those numbers, but it's all thats available to work with. So you have a 50:50 chance to get a ring or a shitty med/scroll. Among that 50:50 chance, you then have a 1/8 chance to get the ring you want. Then you have to hope to get a good aug (or two if you can get double augs) as negative augs are available.
