Looks like you pretty much already found the answer but thought I'd verify that paints could be possible if he is dominant white.
Heterozygous dominant white over black is what makes up paint to my understanding. Sometimes the dominant white is more leaky than other times so spots may or may not show up. Austrawhites are a great example of how you can get spotted babies crossing a bird that is dominant white over a black bird.
Dominant white chicks tend to be more yellow looking than recessive white chicks. The gold based ones can be more gold tinted for sure but I've found it is the gold based recessive white chicks that really look more like buffs as babies. I would guess from your description that Jane is probably recessive white but you never know. I guess the babies should offer some insight anyway!
Here is a recessive white chick I hatched on the far right (I believe gold based). Ignore the one labeled partridge....I was guessing at what they would be and though I was right about the rest the one I thought was going to be partridge turned out to be more blue looking than anything else. From what I've read a lot of recessive white babies are partridge underneath the white so those sort of lighter stripes you can see on her back I'm guessing are from some partridge influence on the chick down.
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And here are some of my chicks hatched from paint parents. Both the paints and the pure yellow/white are carrying at least one copy of dominant white. The little silvery white one I'm not exactly sure what it is other than silver based (it turned white I'm just not sure if it is dominant or recessive white.....it looks more similar to the silver based recessive whites I've seen though).
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Hmmm I wonder if I assumed your white was a recessive white. Most white silkies are and you can't make paint with a recessive white over a black. If your rooster is dominant white and you have him with a black hen than paint babies are definitely possible.
Sorry if I made things confusing before!