i reckon improve your soil, so it wets easily and stays moist.
preparing carrot soil before sowing:
- add bentonite (or slurry from local red/yellow clay)
- add gypsum
- add horticultural grit
at the moment to improve soil wetting and moisture capacity
- a thin watering with either bentonite or thin slurry from local red/yellow clay
- a sprinkle of gypsum
as mentioned before, i think that watering (outside) with a fine nozzle doesn’t wet the soil. a tiny excavation with a finger (post watering) should show. i use a watering wand that produces large water droplets—quickly wave it over the soil to water—and the water penetrates. a fine spray wand/nozzle used to water for an extended period doesn’t do the job either, as the water pools, and the soil develops a fine crust layer which becomes even harder to wet.
alternatively, invest in a misting system that senses when moisture is needed, or setup with a reasonable timer.
another possibility is using setting up a tunnel using clear plastic but, they seedlings might possibly cook.