1. It flies out of Minneapolis but isn't Delta
2. It flies into Trondheim, the nearest large city to the island where my relatives gather each summer
The lowest-priced tickets get only buy-on-board food, but if you're flying from Minneapolis, the flight leaves at 7:30PM and arrives in Iceland at 1:00AM Minneapolis time, so I didn't need to eat anyway.
I took a friend's advice to do my free stopover on the way back rather than on the way over. The reason is what I said above. You arrive at 1:00AM Minneapolis time, 6:00AM Iceland time, and you're a zombie. Better just to grab a cup of coffee and a pastry and save your sleeping for your final destination.
On the way back, you have only two hours of jet lag to adjust to, and you arrive in the late afternoon, so you have time to stroll around the city for a while, have dinner, and go to bed at a normal time, so you can start the day fresh.
I did the Reykjavik city tour on the first day, the Golden Circle on the second day, the South Coast and glacial lagoon tour on the third day, and the Blue Lagoon on the way to the airport on the fourth day (it's closer to the airport than to the city).