But that wouldn't answer the OP's questions about their existing population.

Also...

Have you ever worked with EMS? It's the last resort of the desperate. You burn money and time searching for a needle in a haystack.

It's useful for creating variations for narrowly targeted objectives with easy phenotyping. Say a color variation in a flower or a herbicide resistance in grain.

Ploidy also matters a ton for if the mutations will be able express at all. Saffron for example is a sterile triploid. J. Artichoke is a hexaploid- double the number chromosomal copies.

Side note: For Saffron the outlook for breeding looks to be very good. They have identified the parent species Crocus cartwrightianus. It's also in a 2n diploid state. Converting the 2n to a 4n and then crossing to make new 3n cultivars is theoretically possible.