I've spent as long as 2 hours in Immigration/Customs landing on afternoon flights into LAX. Landing after A-380's (or on one which you might be) increases the amount of people in there. So unless you have special status (like Global Entry), there's a chance you won't make it. With GE, passing through Immigration/Customs and collecting checked bags takes 15-20 minutes.

OP would be on an A380.

There is a Delta nonstop, LAX-MCI, that leaves a couple of hours later but would arrive only 29 minutes after the US Airways connecting (Phoenix) flight.

With Global Entry, I would be comfortable with the almost 3 hours to make the US flight, bags checked through or not. Wouldn't pack anything I absolutely needed overnight in checked bags, tho.

You can check the average and maximum wait times for Customs at this website. Depends on time of arrival, which terminal, and you can also look by month, day of week, or date.

http://apps.cbp.gov/awt/index.asp

When I returned to LAX from Australia, customs only took around an hour and a half. However, I would say it depends on what you claim and such. I didn't have really anything to claim so it was pretty smooth.

Only in the USA can the word "only" be in the same sentence as "hour and a half" when describing customs.