Well, it all sounds good. I didn’t get a single carrot to germinate. I am going to try growing some in a pot, so I can roll them into the shade or bring them in if the temps get back to really hot.
This fall, I will plant some in the winter garden along with the winter lettuce. So far, the only time I have been able to grow a decent crop of carrots is the fall through winter planting. Spring time crop always fizzles.
I know you used raised beds, but for spring carrots try raising a row 10-12” wide, and a few inches high & flat across the top.
Just lightly roughen up the surface, barely touching it with the tines of a garden rake; then use a salt shaker to sprinkle the seeds and lightly smoothen the surface with your hand; then cover with a thin (1/8” or less) layer of grass clippings. Keep damp.
The seeds should be deep enough just by falling into the spaces between the soil particles then being covered by the grass.