I was never able to convince TK to contact UA about opening award seats. I thought my case was pretty clear cut: I originally had a BDL (Hartford, CT) to DEN segment that was changed into a BDL-ORD-DEN segment. When I contacted UA, they didn't even entertain the idea of touching my ticket and insisted that only TK could do anything. This is with multiple HUCAs. Then, the more I went down the rabbit hole, the more I realized that I could end up jeopardizing the entire itinerary so I stopped pushing.
It took a few calls to get TK to confirm any changes correctly (I called different times during the day/week because I wasn't sure if there was an A and B CSR Team). My experience was that it didn't matter what UA says is "confirmed". If there's an issue with TK, you need to call them repeatedly until they don't see any issues. Ask them to email you the itinerary after every call. When I had issues with mine, I could see both canceled and rescheduled flights on the itinerary. When everything was fixed, the emailed itinerary was correct (dates, times, flights, no extra segments, etc.).
Finally, when the TK side is absolutely confirmed, call UA and ask them to clean up your reservation. This is what prevented me from checking-in 24 hours prior to the flight and prompted me to go to the airport. The phone reps may not be able to fix this but I also didn't know it was the issue at the time of my call. Apparently, when there are multiple flight/schedule changes, the canceled flights are still attached to your reservation and UA may not be able to issue the boarding pass. They also may not be able to do this until 24 hours prior to the flight.
Steep learning curve on this one!