For those interested: I wrote to QR Support on Twitter citing the two PNRs and asking them to confirm (a) that I meet their requirements for transiting Doha despite being on separate tickets and (b) that I would be reaccomodated by them in case of a missed connection.

They confirmed “there is no issue” and I am “confirmed and good to go”, so I now have that in writing from QR. If I end up traveling, I will carry that message with me, along with a copy of the official through check-in policy.