You are probably not going to come up with a whole lot of options there. Posting exact dates might be helpful but I doubt you'll get any different results. Here are the routing rules from expertflyer. You might tinker with it a little on the multi-city search and try a US flight to TUS then a UA flight to DEN
WRA14N10 148.00 296.00 R UA ROUTE:0003
VALID SINGLE CONNECT CITIES FROM: PHX TO AUS
DEN DFW HOU SAT TUS
ADDITIONAL RESTRICTIONS ON ROUTING:
NONE