It would be nice to understand enough about POS availability to be able to game it.
OP mentioned that a general inquiry for availability returned seats, but when his PNR was brought up the availability disappeared. Have others seen that behavior?
If so, it at least used to be trivial to create snippet PNR's that cover a piece of an rtw not including the starting point, with a down-trip carrier. Just call the carrier, tell them you're going to add a couple of segments to an existing xONE (that they didn't issue) and ask for a res for the seats pending reissue. Call them back with the ticket numbers a week later.
Others have posted that seats are available or not depending on which res location you call. If those postings were real POS issues (and not simply that the first res agent and/or the technology at that location were lame) the work-around is simply a long-distance phone call to the right res office. A sticky list would be in order.