You should be able to book the same itinerary on both airlines.

Search on ual.com award booking for both as that's the place to find Star Alliance awards. Since multi-city search tends to not be that great, you should search one leg at a time putting it in as one ways.
1. DAL-HNL
2. HNL-Medford
3. Medford-DAL.

Write down all the flights you want.

You can then try booking on ual.com putting in the legs you want with dates using multi-cit. If all the flights you want come up that way, great! It should all cost 40k UA miles. Multi-city tends to be a little quirky so you may have to call and give the agent your flights.

With US Airways, you have to call and give them your flights. But you are allowed a stopover in an award on different regions.

Expect some confusion and resistance from the agent. It always happens when you're not booking the standard out-and-back itinerary. Just be diplomatic and sound confident that it's allowed. Quote the relevant rule allowing you to do what you want. If there's trouble, just call and get a different agent.

Like I said, I have gotten them to let me do all kinds of crazy routing so this one should work

Good luck!