On non-refundable fares, there are no loner change fees and your fare credit is 100%. So also long as you plan to travel, the risk is low.

As for the issue you are seeing, it could be a fare combinability issue between the partner fare rules and UA fare rules. The specific fares available / needed can be an issue.

Don't expect the earlier agent to call back. Worth calling again and asking the agent to call the fare desk to get a better answer.
If you state you can see the fare offered on united.com, there is a good chance the fare desk will make it happen at the same price.

What is the other carrier? All normal connections?

I have booked fully refundable fares with UA and LH with no problems for a trip I did eventually cancel.

One thing to try is book this a multiple city in the advance search or try Google Flights. Sometime those work better.