You'll run into the heart of the NFL season, when division championships and playoff berths are still in play. If you're going to run a full 24 hours as a non-points event outside the regular season, run it the weekend before the Rolex, on the same weekend as the NFL's conference championships. Start at noon Saturday and you'll be done hours before the first game starts. The track is already gearing up for a long week anyway.
I think if NASCAR got serious about doing it, Daytona circuit would be the easiest option available to them.
Option 1: At Daytona 24 hours, with all 3 series running, 48 car field, top 16 in standings get in from the year before, 6 playoff bonus points to the winner, 3 to 2nd, 1 to 3rd (no other points). IMO I would scrap the exhibition Clash (that's a really prime spot weekend after the Superbowl imo to be wasting it on a pretentious 20 car plate race that nobody cares about imo) The doubling tripling up on plate races Practice, Clash, Duels, then 500...knock it down to Practice, Qual, 500 imo. The Daytona 500 is still King, but really...they don't need 2 weeks to go plate racing imo. Something BIG and different like this would build much more interest by everyone alike going into the 500 imo. This would be a really cool added element to the start of the season.
Option 2: For those that don't want Daytona Speedweeks touched. They could request to add a class to Rolex 24 in only the Cup cars (8 to 10 cars max) and run with all of IMSA. Field size concerns probably got mentioned at that point, but who cares, people want to see it imo. I don't think 8 or 10 extra Cup cars out there will destroy the racing with a 57 car field vs 47. Rig the cars with lights needed for the night, and windshield wiper

. This might be my favorite option. To see the variety of cars and top drivers on the same track. This would not be a points paying race, but a very cool competition for the Rolex watches and bragging rights.
Option 3: Dream scenario long shot. Go huge and take it INTERNATIONAL to France for the LeMans 24 hour Circuit De La Sarthe to combine with IMSA. Adjust the schedule as needed for Cup and take the top 10 cars in the points standings up until that point (added regular season reward). The 10 Cup driver's do a broadcast fantasy draft of 3 other driver's from any NASCAR series the week before. If more time is required to get the cars shipped over there and ready, then it's the top 10 in standings from last year, and they fantasy draft the driver's they want during Daytona Speedweeks. This would be a large stride to broaden the current reach of NASCAR and not the first time they've had International success.
The Rolex 24 really has a prime slot the weekend they occupy before the Superbowl, NASCAR could have the same for their own endurance race the weekend after Superbowl, or get in on the action with IMSA. I don't think it's an impossibility if they decided to pursue it. And, I hope they do! They seem willing to experiment at this point, so why not experiment with something like this?