I'm taking on a project going to attempt to breed Helen's Hybrid (seeded) with Blue Java (as the pollen parent).
From my research, I believe moderate fraction of the offspring will be tetraploid, which can then be hybridized again (with seeded normal diploid) resulting in seedless (edible) triploids in the third generation.
The reason the fraction of tetrapoids would be higher is that a majority of the triploids parental cells that undergo meoisis fail to even properly form normal haploid gametes, so the natural percentage of gametes that escape unreduced then becomes much higher relative to the total number of viable seeds.
Alternatively, it possible to just treat the apical shoots with either Colchicine or Oryzalin (right concentration) to double the number of chromosomes (to tetraploid), then breed one more to get an edible triploid that is now seedless.