If this is the return, then my suggestion is to relax.
AA has eight non-stops daily (every few hours) and if you miss one you will just be put on the next one. Plus they have tons of connections via DFW (and more if you include ORD or US via CLT or PHX).
Unless you absolutely positively have to be in LA before lunch the day you return, I wouldn't worry about it. And I certainly wouldn't buy a ticket when it's the airlines' responsibility to sort this out. Again, unless you just have to be in LA early on that morning.
Finally, I looked at some random dates and can't find the change you are talking about. AA still has their first flight at 7:20 a.m. on all the days I checked (for some strange reason, Alaska lists that flight at 7:00 a.m.). But nowhere can I find the change to 5:50 a.m. At least no time this spring.