I posted my experience last fall with separate ticket protection going from AA to BA here:
AA to BA protection separate booking - experience
AA flights were delayed by weather. I dealt with AA agents over the phone.
Key takeaway from the experience which might save time in the future...
AA needs to take over control of the other OW ticket, so the agent needs your ticket number. In my case, they merged it into my existing AA PNR, and I was rebooked as if a missed connection on that itinerary.