Transcontinental redeyes are not a big deal, in fact LAX-DFW is even less a big deal. I work overnight on some occasions and just go to bed early the next night. Same with redeyes.
Although it is not very nice to sleep a few hours and wake up the next morning on final approach into another airport, but there are worse things in life. Book yourself in a out of the way seat, get in the plane, try to sleep ASAP and get up and go in the morning. I do not recommend using pharnaceutical agents as their effects can last well into the next day. Good earplugs are probably cheaper and more effective. Cheers.