My last flight out of LAX was in '07 on a Monday evening around 6pm. I've been through the airport several times and last time security was a breeze. I know it's definitely not like that every day, but from the time of arrival to when I got to the gate was only a space of 20-30 minutes.
FWIW, flying Alaska on a Monday around that same time, just last month, security was good too. We were beyond late (we are "get to the airport 90 minutes before flight-time" people), got to the gate after they were scheduled to have boarded (for some reason they were late in boarding and we had 3 minutes to wait before they boarded).
As we checked in for Alaska, the agent helped hubby take the bags over to the conveyor belt (it's not behind the desk there, you actually take your bags there) while I did last minute carryon things. The TSA people were lovely. Hubby did have to be wanded (turned out to be the zipper on his shorts causing problems with the machine) but they did it fast, and I almost had to be wanded (my 1.5" barrette caused the metal detector to go off), but once we were through, the TSA agents helped us get our kid's carseat back together (had to loosen the straps or something like that to get it through the machine? I wasn't a part of it), helped get shoes to the right people, helped get our laptop back in the bag, etc. Nothing but kindness, and I quickly told a guy to not let his wife take them for a "haven't been to DLR for years, let's go for a one-time one-day visit on xmas day" thing, and we ran for the plane.
That's the second time out of LAX with Alaska and I have nothing but good things to say about them.
That said, we were there late because of the traffic leaving around the time you're thinking of (on a Monday), but there was also rental car return going on.
Are there HOV lanes on the trip back to LAX? If so, and especially since the drivers for
Disneyland Express should know the roads a bit better than your average tourist, I would go with THEIR suggestion. So if that means 3:40 I might go then. If they say 2:40, go with that. But I'd call them, definitely.