Anyway, here's why I'm asking. You were wondering how to increase the white in the offspring. I have some thoughts... hoping @AugeredIn will not laugh too hard
The birds are both reportedly cameo BS pied white-eyed. Now just talking about the leucistic genes (not the cameo, not the BS genes) in these birds...
Starting with the male bird:
WE genes will give white eyes in the train, as you know, even if only one gene is present, but sometimes that will only result in a few white eyes. So if his train is "mostly" white eyed, then let's assume for the sake of argument that he is carrying 2 WE genes.
[At this point, we can have a long discussion about whether there is a variant WE gene that results in silver pied birds when it occurs with the correct other genes, which we could call a WEsp gene, or whether such a variant doesn't really exist...] But in this case, since the male doesn't seem to have much silvering if any, let's assume he doesn't have two of them, and maybe doesn't have any of those variant WE genes, if they do exist. He does, however, have to have some kind of WE gene that is causing the white eyes in his train, and most likely has two of them.
We also know that having WE genes seems to increase the amount of white on birds, not just the white eyes in the train.
When we see a "pied" bird (phenotype), we don't know for absolute certain what genes that bird is carrying, unlike a "white" bird, which we know MUST have two white genes. We know that in general, a bird with two pied (P) genes will usually only have a few white feathers ("dark pied") and the more visibly pied birds ("loud pied") are thought to have a white gene combined with a pied gene.
Silver pied birds are thought to have a white gene, a pied gene, and two WE genes, probably a variant WEsp gene but there continues to be some debate about that.
The darkest birds have only one pied gene or only one white gene, which can show up as only one white primary wing feather, a white chin patch, or with no visible white at all, just completely hidden.
So theoretically, the male bird would be thought to have one white gene paired with one pied gene (resulting in the pied appearance) and two WE genes, resulting in the white-eyed train. But you are right, he doesn't have lots and lots of white on him, despite the fact that he has two WE genes. So I am wondering (@AugeredIn , here's where I'm hoping you won't laugh) if it could be possible that he is missing either the W gene or the P gene? What if he has two pied genes plus two WE genes which are increasing the amount of white to more than we would normally see on a dark pied bird, but less than we would see on a W-P 2 WE bird?
You could test this by breeding him to a white hen... the white hen must have two white genes, and must pass one to her offspring. If the male has a white gene and a pied gene, which is what we would normally expect, then some of the babies should be white and some loud pied white-eyed (but probably with only one WE gene). If no white chicks ever turn up, then the male would not have a white gene. If you can find a white hen from a cameo breeding you will still get cameo chicks. (I'm going to set aside the sex-linked discussion here and focus on the white though.)
If by some chance the male IS missing the white gene (I dunno?), then adding a cameo (hidden color) white hen will add the white gene to your breeding and may increase the amount of white on your pied offspring. If you can come up with a white from a cameo silver pied breeding, it may also add the variant WEsp gene, assuming it exists, and will certainly bring at least a WE gene with it.
This is getting too long for one post... I will discuss the hen next.