Sorry to see you lost most of your carrots! I wonder if they rotted because they started out looking so moist or maybe because of all of the rain we've had this year? I planted ours out about the time you posted the picture of your carrots to be planted. We've been staking them and it seems the more we stake, the taller they grow and they're loaded with seed heads and ladybugs.
I stored them over the winter in the fridge which may have been a factor. Next time I'll try sand and a cold place. Glad yours are doing great. Can't wait to see the seed heads, etc.
I stored mine in the fridge too and they came out perfectly fresh, although they were rooting. In the Fall I wash all of the soil off and spread them out on a tea towel to dry for half a day. I then put a few paper towels in the bottom of a grocery bag before filling with carrots. I store them in the crisper with the top of the bag mostly open. I've done this since 2009 and have had great results each year. Last Fall I left some in the ground. They survived our warm winter and are forming seed heads, but aren't as lush as the ones I transplanted in the Spring. Not sure what kind of weeds you have around your garden but I haven't had a problem with cross pollination so far.
Thanks for the tip about the paper towels and open bag. Mine were probably too moist as you said. They didn't root at all in the fridge.