Another option could be a different US that ends up having the Rio Grande Republic join as a state (but may not be possible with a PoD after 1836), in which case you have a heavily anti-slavery base south of the Rio Grande - then you could have Southwest Texas declaring neutrality or even proclaim for the Union, as they have a greater source of support nearby. (Also the Texans there are afraid that, if they don't do so, that the Rio Grandese could annex the Nueces Strip if they remain anti-Union).