There is nothing in the OT or PT about sourcing of lightsaber crystals. We only know that many Jedi Padawans obtained their's in the ice caves at Ilum from the Clone Wars. And, both the clone wars and rebels show Kyber crystals being obtainable on planets other than Ilum, including Lothal. All of the assorted lightsaber crystal mythos, beyond that, is apochrypha rooted in EU (especially RPG) sources.

The only reference pre-ROTJ is a reference to a decorative crystal on a lightsaber hilt in the novelization of A New Hope. It wasn't a functional part of the lightsaber. My point being: that luke's lightsaber in ROTJ makes a different sound than the one he had in ANH and ESB is immaterial and has nothing to do with the "kind of crystal." The idea of lighstaber crystals wasn't even a twinkle in Lucas' eye, let alone different kinds having different properties, let alone their being rare of unique to certain worlds.

Even with actual canon sources to retcon with, you couldn't argue that luke was unable to obtain a Kyber crystal because Ilum is blockaded.