I live in NY and similarly wanted to move a Coverdell to a 529. I was actually doing it a little at a time as I preferred how the money was invested in the Coverdell over the 529, I did actually do a transfer (rollover?) for a few years where I provided the cost basis. One day I was talking to a rep on the phone and was told if I simply withdraw the money from Coverdell and then within two months contribute it to the 529, the cost basis will get reset. This really did not make sense to me, but I called and was told the same thing from a second rep. The 529 does not really know where the money came from. As far as they are concerned, it's a new deposit. When I do my taxes, in Turbotax, I indicate that my withdrawal from the Coverdell was contributed to a 529 and Turbotax, therefore, does not treat it as a taxable event.
I am still leery, but that is what I was told. But, I do plan to use it all for qualified withdrawals, so the cost basis really doesn't matter as far as I'm concerned.