First, where and when did these Heidel/Hadels settle first in the US? Perhaps this would help to determine the possibility of whether any might have a connection to them.
German immigrants with a combination of first/middle names such of Johann, Fredrich and Carl appear to have been very many, as you probably well know. Likely the English/American use of any of these names became simply and singly John, Fred or Carl. Probably the most unique and lesser used of these being that of Carl. My great grandfather’s name has been recorded in a family record (probably from about 1904) as ‘Carl F. Heidel’ – the ‘F.’ for Frank. So far, in only one instant that has been found, has his name appeared as ‘Carl F. Heidel’. When he died, all references for him became simply ‘Frank Heidel’ that I have found and that’s what appears on his grave marker. Where there is a dilemma for me is how was his father’s name used, as little record of him appears that I have been able to discern. The same family record names him as simply Christian Heidel. Given what I have found with Frank, I almost have to assume he is anonymous. I do not appear to be the only one that may have concluded this because in some familysearch.com records he appears as 'Mr. Heidel'.
Certainly the Johann Fredrich Carl Hadel having married a Rebecca Seywert would add significantly to the uniqueness for the name of the couple – if both have been referred to by their first names together. Hmm, could this be why a wife can be considered the better half? <grin>