In my opinion, "seem" here is a link verb. So "seemed" is the past tense of "seem",it's like "was" to "is" or "am".
After the link verb,there can be verb+ing form following.And you can also consider verb+ing as a adjective.
The sentense can be changed to:
No southern governor, except William Gist of South Carolina, was willing to lead the South out of the Union.
Although it loses the meaning of "seem", it's much easier to understand the grammer.