I suggest that transmuted artifacts are added back to the loot table. It will still be technically max one artifact of a kind.
I also suggest that artifacts in crystal chests not looted also gets added back to the loot table, or not generated until chest is opened.
Players who are willing to spend 10-15 transmutation scrolls should get a chance of getting the artifact they want. It also removes the confusion from players getting a ring, thinking it’s a bug. It will also create a more consistent drop in line with other transmutations without breaking the uniqueness of artifacts. If however all artifacts are available to the player, such as using Ring of Wealth, then it can become a ring.
Yes, those are valid concerns. One alternative is to only reroll them once all artifacts have been generated, also increasing an “artifact reroll counter”. All artifacts will also internally keep a copy of this counter.
If a chest is opened contaning an artifact where artifact.counter < current counter, then discard it and generate/drop a new artifact.