It's theoretically achievable but would be extremely expensive and time consuming.

Hmmm... Here a quick stab at methodology to achieve your aims.

To start if you have the funds, a full sequence of several lines of J. Artichoke and maybe a few accessions of diplod wild types that can make a viable cross. Then create an extremely high density SNP marker profile of the individuals.

Next generate 6n x 2n crosses to initiate the breeding project. The resulting 4n progeny could be further reduced to 2n via haploid creation techniques. Irradiated pollen parthenogenesis works in the genus. So there's a possibility it will work.

Once you have it in a 2n state it's time to figure out the self-incompatability mechanism. With the mechanisms defined, a introgression strategy is possible to get the original 6n genome into three 2n lines using the SNP markers.

From there you can do all of the gene discovery and breeding much easier. You can identify genes of interest and manipulate them by breeding the 2n lines. Seed production should be around 1,000x better than the original.

You can always recreated a 6n line by doubling a 2n plant with colchicine to 4n. Then crossing the 4n x 2n plant to generated a 3n plant. Doubling the 3n plant with colchine creates 6n again.

All together it would cost around $3-5 million USD per year and take around 15 years to accomplish if everything went smoothly.