The Southern states had a lengthy list of grievances, not the least of which were numerous violations of article IV section 2 of the Constitution.
The only relevant question is did those violations render secession legal?
Texas v. White says no. But that opinion seems to be founded in the notion that the territories/states/peoples were bound at the hip in perpetuity simply because there is some commonality in purpose. Yet it also says.."There was no place for reconsideration or revocation, except through revolution or through consent of the States.
So assuming it's 'illegal' to secede, what, if any remedy can the General Government have legally sought?
According to Kentucky v. Dennison, none.
"...there was "no power delegated to the General Government...to use coercive means to compel" a state governor to act.
Congress passed numerous fugitive slave laws, provided a number of ways of enforcing those laws, and in every case were an individual state tried to restrict the enforcement of the laws the courts ruled against them. If that was a grevance then it was a made-up one.
The only relevant question is did those violations render secession legal? Texas v. White says no.
Not entirely accurate. Texas v. White does say secession is legal if done with the consent of the states, as you pointed out in the quote you provded.
According to Kentucky v. Dennison, none. "...there was "no power delegated to the General Government...to use coercive means to compel" a state governor to act.
I'm not really sure why you picked this particular case since it has nothing to do with secession. If you're looking for Article IV support then perhaps a more appropriate case would be Prigg v. Pennsylvania where the court ruled that individual states could not enact laws that interfered with the enforcement of the fugitive slave laws. However, the court also ruled that the fugitive slave laws were federal laws and that states could not be made to enforce them.
Kentucky v. Dennison war overruled in Puerto Rico v. Branstad.
Another "swing and a miss" for Chief Justice Roger ("Mr. Dred Scott") Taney.
In fact, most seceding states had no list of grievances -- zero, zip, nada.
Those few which did produce "Reasons for Secession" documents included no past grievances of any seriousness to justify secession, but clearly showed their only real concern was protecting the future of slavery against possible actions of those nasty, rascally black-Republicans.
So it was unconstitutional secession "at pleasure" preceded and immediately followed by many acts of rebellion, insurrection and/or war against the United States.