Calling all carrot breeders!

So, I'm attempting to produce a blend of open-pollinated carrot seed simply for my own use.  I know carrots will typically grow flowering umbels in their 2nd year to produce seed.  I tried to get a head start by using about a dozen or so store-bought carrots of the right size, shape, and of different colors/sources as my foundation (with crowns).  I already had a long hilled row in my garden of organic plant matter that I wanted to speed up decomposition on, so I shoveled dirt over top, planted a lot of potatoes/slips (which are doing well), and covered with straw to retain moisture.  Then, I inserted the carrots into the soil up to the crowns.  I was hoping for a flush of greenery, but it's been nearly a month, and so far, nothing.  

Now, I have a couple theories as to what might be happening...that is nothing's happening.  One, I just need to give the roots more time to send out the hair/feeder roots before they grow tops.  Or two, the carrots will need to overwinter even though they're mature carrots, they might not be old enough?  A few of them were in the fridge produce drawer for 3-4 months & started leafing out a little in the humid bag, but we have had no rain for near a month.  That's why I had to get a soaker hose.

Anyone have experience with growing store-bought carrots for seed?  Do you think they will cross pollinate amongst each other if they ever grow?  I remember reading about some cytoplasmic male sterility in carrots, but these are organic, so I'm hoping there wasn't any growth inhibitor sprayed on them.  As of now, the way I'm looking at it is, they'll either grow eventually & maybe produce seed or they won't.  Maybe some will rot or maybe they'll still be there when I harvest potatoes?

Ideas?

Your time window for carrot transplanting is minutes (not hours or days) and the carrot should not be washed.

Likely your market carrot was out of the ground too long and was washed. you would know in a matter of days if the carrot would survive relocation.

They were certainly washed, but I thought since some people grow carrot tops from store bought carrots in water, I thought surely the whole root would be better.

Update:  I have confirmed 2 carrots have leafed out.  Hoping for many more if I'm lucky, but it's a start.