Yes. Sex matters.
Taishu often has male flowers. Taishu was the male parent of JT-02.
My proposed cross would again use Taishu as the male parent. So it would be JT-02 (female) x Taishu (male), though any male-flowering PCNA would presumably work.
We can assume that JT-02 already has 3 non-astringent (NA) alleles (out of a total of 6) from its male parent, Taishu. When back-crossing JT-02 x Taishu, we’re expecting only ~5% of the gametes from JT-02 to have all 3 of these NA alleles. Meanwhile, 100% of the gametes from Taishu will have 3 NA alleles. So ~5% of the seedlings should be NA with 6 NA alleles.
Cardinal is a Japanese PCNA but it is female. The male parent is the "hybrid male seedling (JT-02 X Male Rosseyanka Seedling). We’d expect 100% of the gametes from Cardinal to have 3 NA alleles. So far, so good.
The question is: What about the male hybrid?
The male hybrid is a cross of JT-02 x Male Rosseyanka Seedling. We can assume that this male hybrid has 3 Astringent (A) alleles from its father, Male Rosseyanka. This hybrid may have received 0, 1, 2, or 3 NA alleles from its mother, JT-02. We can’t know the number, but there’s roughly a 95% chance that the gametes from this Male Rosseyanka hybrid have only 0, 1, or 2 NA alleles. But without the full set of 3 NA alleles, there is NO chance for an offspring of Cardinal x Hybrid Male to be NA.
On the other hand, there’s a ~5% chance that the genome of this JT-02 x Male Rosseyanka cross actually has 3 NA alleles. In these 5% of cases, there’d be a further 5% chance that the specific gamete used in the cross of Cardinal x (JT_02 x Male Rosseyanka Seedling) has 3 NA alleles.
Bottom line: It seems to me that to a 1st approximation, there is a 5% x 5% (i.e., 0.25% or 1/400) chance that an offspring of this cross is NA.
Note that the number of NA alleles in the JT-02 x Male Rosseyanka seedling parent is fixed. There’s a ~95% chance that the number of NA alleles is too few (0, 1, 2) to produce ANY non-astringent offspring, ever. But there’s a 5% chance that the seedling parent has 3 NA alleles. Only then would there be a further 5% (5% of 5%) chance that the seeds offered for sale can produce a NA seedling.
p.s. Yes, the OGW Cardinal is a Japanese PCNA Kaki. It is my belief that Cardinal is a synonym for the Japanese variety Soshu. Assuming my arithmetic’s right, Shoshu’s ancestry boils down to 3/8 Fuyu, 1/2 Okugosho, 1/8 Fukurogosho. Its mother is Izu, which is 1/2 Fuyu, 1/2 Okugosho.