Between manual gathering and Crush specialists, keeping Crystal Fragment stocked isn't hard. The Crush route is less effort once you've assigned the right Pokemon to the job.

Rare crystalline shard

Raw Material
MoveRock Smash / Rocky Ridges Mines
Rock Smash Crush specialty Rocky Ridges
Requires: Unlock Enhanced Cut move
Dream IslandDream Island gathering
DugtrioCrushGravelerCrushOnixCrushGeodudeCrushCranidosCrushAurorusCrushRampardosCrushLarvitarCrush

You can craft Mirror Ball using Crystal Fragment. These 1 recipes are mostly Utility items that help fill out your island.

1 recipe
Mirror BallUtility
Gold Ingotx1›Crystal Fragmentx1