Yep! You might have gone a little overboard on seed sowing.
The safest way would be to cut the heads off about 99% of the seedlings. But, Papaver is one of the genus of poppies that do transplant. You could maybe take bunches of seedlings out (you will be sacrificing some of the seedlings but not as many) by digging straight down and out an inch or so and lifting a group to transplant someplace else. You will never have the recommended spacing but with fewer plants, they will do better.
