This is the first time I've ever grown shallots. Most everything I've ready says they don't grow well here in the South. But my feed & seed had some for sale this spring and because they usually only sell stuff that grows here I bought two sets, variety Nero (an F1). Cost me all of 25 cents. Why not? I'm such a big spender.

They've done well and multiplied and today I saw three scapes with the little flower heads on them and cut them off since I can't use the seed. The plants are still green with no sign of dying back yet. My question: should I have cut off the scapes? That hasn't been addressed much in articles I've read online. If I let them stay will they form a hard core down the middle inside the shallot?

If they went to seed it's just like the onion.
It thought it went through 2 seasons and bolted.
Not good naturally.

Have a look for information on potato onions. They are the same species and some regard the biter ones as potato onions and milder ones as shallots. You can grow them no problems, could get some to adapt to your location better if grown from seed. Look up Green Mountain potato onions and check out the open source seed initiative forum, also the old Homegrown Goodness forum.