The highest capacity on that route is on AA, not B6 or VX, so check their prices. B6 has made some moves lately that makes me think they're running cash poor and need to raise prices until that situation is resolved, so I wouldn't count on them. AA essentially runs a shuttle service, with 13 or more flights each way per day; they also have brand new aircraft on that route, too, with very nice IFE. For a random week I picked in mid-April, they're charging $419 RT per adult on pretty much all of their flights.
My last trip to LAX was $380, and I haven't seen prices on transcons below $350 (RT) in quite a while, so $400 is about what I'd expect to pay. If you're flexible in both date and which flight you can take, you can watch and wait to see if they go down, but $420 is a price I wouldn't have trouble with.