It really depends.
You have a very small core of guys who like the Redeye turns because they live in base and want to be back home every day. A Redeye turn classic example is our ATL-PHX, basically a CDO (Continuous Duty Overnight, Nap or High-speed, depending on what regional you came from). It leaves base around 8 or 9 p.m., blocks into PHX around midnight Eastern time, leaves at 0200, and gets back into ATL around 0600.
With your rig, that would be basically 5.5 HOURS of pay on our side of the fence per duty period. 3 in a row over 4 days would pay 22 hours, which is in line with what most of our 737 lines do, 5-6 hours per day credit, but they don't leave until late and get in early, leaving you the whole day,,, allegedly. I'd collapse and be out most of the day after those, but I'm getting old.
Pre-bankruptcy those things used to pay around 7 hours a day at Legacy carriers, my Dad made 10 years of his career doing those, flying 2 back-to-back over 4 days with 24 hour overnights on the West Coast, making it a 28-hour 4 day. 3 of those a month was 84 hours of pay with 18-19 days off, so they went senior.
Here, they do NOT go senior unless they're on a LINE in ATL. In MKE, they go mid-level seniority, a few CA's and F/O's snatch them up, our MKE F/O rep is one of them. In ATL, there's enough people that like them that they don't get past the top 1/3 of each seat's seniority list. In MCO, the one redeye that was on our lines for the first time ever went almost very bottom of the pile junior.
When Daily open time comes open every month, the very first thing that happens is those line holders who have them scattered on their line drop as many of them to open time as they can, which forces our reserves to fly them, which is a constant complaint with the circadian rhythm "flipping". (We don't have to get someone to pick up our trips if there's good reserve coverage, we can just straight give them back to the company and wait for something else to come up that we like better).
For those of us in smaller bases, there's not enough reserve coverage to get rid of ANY trips, I haven't been able to drop anything the entire month. Therefore, if you get stuck with a redeye somewhere, you're probably just stuck with it.
As for how it will work at Southwest, it really depends on how they build them. With their aversion to soft time and desire to keep everyone maxed out, I'd be shocked if they built them into line of all red-eye flying (which is what they SHOULD do). Also, 40 redeye flights PER DAY sounds a bit high. Even if you had 10 city pairings originating red-eyes at night, you'd have to send them to BWI/MDW/MCO and a 4th East Coast base to get near 40. Do you have 10 West Coast cities that could originate red-eyes to every East Coast base?
Maybe that's a combined number with both of our companies integrated...?