I would recommend moving Clement Vallandigham to the 1869-1873 slot. Craigo's updated entry on the 1868 presidential election list Vallandigham as one of President Seymour's critics. It would be very unusual for a Secretary of State to openly be criticizing his president. (Also, the Fugitive Slave Treaty that Vallandigham negotiated is listed as an achievement of President Hendricks, which suggests Vallandigham was Hendricks' Secretary of State.)
For the 1865-1869 slot, how about James Bayard? He was extremley pro-southern, so having him as Secretary of State would fit with the Seymour Administration's accomodationist attitude to the CSA. Craigo's revised 1868 presidential election entry also makes reference to a Bayard-Hunter Treaty, so it seems like a Bayard was negotiating on behalf of the United States during the Seymour Administration. (And since Thomas Bayard is also listed as one of President Seymour's harshest critics, that means it was probably his father, James, who negotiated the treaty.)
And on the subject of Thomas Bayard, he could fit in well as Secretary of State either in 1877-1881 or sometime in the 1885-1889 period. (President Hancock might not want a leading doughface as his Secretary of State, but maybe he had to make that concession to the Soft Line Democrats to win the nomination, or maybe Hancock did appoint someone else, but the Soft-Liner Thurman sacked Hancock's chosen Sec. of State and appointed Thomas Bayard when he took office.)
As for the 1937 to 1941 spot, maybe Sumner Welles would work there?
Good suggestions. I have a few questions though. If Thomas Bayard is Secretary of State from 1877 to 1881, then would would be Hancock's Secretary of State? I also agree that however was Hancock's Secretary of State would be sacked by President Thurman and replaced with someone else. But who would this someone else/Thurman's Secretary of State be?
I agree with Sumner Welles as Secretary of State as well. Very good choice.