How about research over the number of days transmute crystals are required for the set, +100 crystals to start research. then it's in your sticker book and you can reconstruct for the normal crystal price. 9 trait crafter, max 3 concurrent researches per character.

A cube or sorts where you can place a 2-3 non recontructed set pieces into a cube and get a random different piece of that same set.

It could further be broken down so that if you put in a couple weapons, you'd get a random weapon from the set. If you put in a couple body pieces, you'd get a random body piece.

I think this is a fantastic idea. Having the created item not be in your set collection would definitely give incentive to still run the content after you've made it, but can be a stop-gap to allow you not miss out on other content in the meantime. It's fair, utilizes the system in a way that requires less coding than a new token/currency system, and is player-friendly without being unbalanced or completely devaluing old content.

After u32 you wont be able to drop stuff that is already in your collection until you collected them all

For exemple, on your first maelstrom run you get the greatsword, well until you get everybother maelstrom weapon the greatsword cant drop!
Giving a definitive max number of run to get what you want