Well, if you start the private stock ordering process, the first question they ask you is what model do you want to start with. And JA-15 is one of the choices (as is pretty much every model past and present), so in that sense, it is a private stock.
And no, the Hollowbody II and the Singlecut Hollowbody (my only two reference points of experience), are best thought of as part way between an archtop and a solidbody. They don't have the ...I forget the word...the top doesn't resonate like on an acoustic guitar and an archtop guitar, but the internal volume does provide a small bit of amplification, so played acoustically, you can hear it a little more than a solidbody, but nowhere near as much as with an archtop.
I am in the same camp as the rest of you guys. I think if an archtop was available in the core line, perhaps with the same maple neck artist pack options as the Singlecut Hollowbody I recently received, I would have ordered that instead. I'm still pretty sure I'm doing something along those lines in a 7 string private stock at some point in the future. Although maybe an SC-J based design instead of the JA-15.