Trying to book an award ticket that involves KE, CI, DL, and VN segments. Specifically:
DL JFK-LAX
DL LAX-HND
KE HND-ICN-SIN
VN SIN-SGN-HKG
CI HKG-TPE-JFK

Using KVS and wandr.me, I verified availability on all the segments I want. Knowing CI and VN aren't available online, I went straight to calling in. Tried two agents, neither of whom could see the KE segments I wanted. I tried the DL website, and was able to find the exact KE segments I want.

I've been able to a PNR for the segments I want, and can look up the itinerary using it. When I look it up, I get a message saying "Award Itinerary On Hold. Please redeem this itinerary before Fri, 18 Oct 2013 to avoid cancellation. Only the SkyMiles member whose account was used to hold this itinerary may redeem it."

Based on that, can I call in with the other non-KE segments I want, have a phone agent add them to this PNR, and book it? Or should I use the evidence of this PNR to convince the agent that there really is availability that they're just not seeing?