I like the idea of Iridescent Gem being a unique item in a sense of it having a unique way of obtaining by deconstructing a staff that is not craftable in a regular way. Unfortunately, you only need 1 Iridescent Gem to activate archives and afterwards you have no real use for them and they just stockpile over time.
As such I suggest making it possible to give Iridescent Gem to Archive Orchestrina to make it be able to provide more knowledge. By hovering over Orchestrina a Build option appears, requiring you to provide either a blueprint or a single instance of an item. Once craft is finished Iridescent Gem is consumed; if a blueprint was given it is consumed as well, if an instance of item was given if would be spit out and Orchestrina would begin to operate as crafting station (its default distilled knowledge would still be obtainable by clicking on it). If item/blueprint was non-prototypable, it would only be craftable while standing next to Orchestrina. If item was prototypable Orchestrina-exclusive tab will appear where it will be possible to request corresponding distilled knowledge which can then be turned into blueprint at the archive puzzle.
While blueprint application part seems obvious, item application can be extended to craft stuff that is not craftable in any other way as long as at least 1 piece of it was obtained and brought to Orchestrina - for example, to craft Archives turf by digging and giving existing one.