Haven't done that specific route, but moved across country before and did a 17 day road trip in the process. My suggestion:

Take the northern route, the southern route on I40 will crush your spirit and make you want to drive off a cliff (fortunately there aren't many). Shouldn't be weather issues in the mountain passes in October, check before leaving. Shoot for Denver on day one (almost 1000 miles - but very boring). Drive until you can't tolerate it, then find a place to spend the night.

Colorado
Utah



Split the rest over 3 days. Take your time through CO, UT, AZ (lots of different routes - get off the interstate); downside is there isn't really a good halfway point (Moab might be depending on how close to Denver you actually get on day 1). Last night in Vegas, then an easy 4-5 hour drive to get to the OC and you should have enough energy to unpack.

Audiobooks are good for staying awake. You're brain is much more engaged than just listening to music.