Taking your last question first, regarding non-Southerners, I think a letter by Lewis Cass of Michigan may shed some light on how some non-Southerners felt during the time immediately before the Treaty of Guadalupe Hidalgo ending the Mexican War, which raised many issues concerning the expansion of slavery.

Cass, later a Senator from Michigan and Secretary of State under Buchannan, and a key proponent of the concept of Popular Sovereignty, wrote a widely republished letter on the Wilmot Proviso which sheds some light on the thinking of some people during this period:

[Excerpts]

“We may well regret the existence of slavery in the southern States, and wish they had been saved from its introduction. But there it is, and not by the act of the present generation; and we must deal with it as a great practical question, involving the most monuments consequences. We have neither the right nor the power to touch it where it exists; and if we had both, their exercise, by any means heretofore suggested, might lead to results, which no miss man would willingly encounter, and which no good man could contemplate without anxiety.” 

and

The question that presents itself is not a question of the increase, but of the diffusion of slavery. Whether its share be stationary or progressive, its amount will be the same. The rejection of this restriction will not add one to the class of servitude, nor will its adoption give freedom to a single being who is now placed therein. The same numbers will be spread over greater territory; and so far as compression, with less abundance of the necessaries of life, is an evil, so far will that evil be mitigated by transporting slavery to a new country, and giving them a larger space to occupy.”

You will note in Lewis' writing, there is no regard, really, for the actual enslaved people.

In terms of the remainder of your question--changing attitudes concerning slavery, I'll answer with regard to Texas, where I have expertise. As Texas was once an independent Republic, it is sometimes a bit of an outlier from the remainder of the American South, as you will see in terms of how some slaves came in to the area after 1827 when it was still part of Mexico.

There was not, in Texas, ever much of any kind of prevailing abolitionist sentiment, aside from that sentiment espoused by the Mexican government in the years following independence from Spain. There is little evidence to suggest that many people in Texas thought slavery was "wrong," either--speaking, of course, of the Anglo settlers.

During the period after the Constitution of Coahuila and Texas of 1827, which outlawed further importation of slaves and actually declared children born to slave parents free, some people coming to Texas adopted a practice by which they "freed" their slaves on paper prior to coming to Texas, but kept them, and there were conditions that their offspring basically were indentured servants to them for the remainder of their lives. Texans actively looked for loopholes to keep the institution going, rather than question its appropriateness.

The very best that Texas really offered in terms of anything that favored the slaves were a handful of legal protections that prohibited slave owners from excessive cruelty in punishments, specifically the taking of life and limb of slaves, and also laws that allowed slaves charged with more significant crimes to be tried by juries. The Handbook of Texas calls that an "acknowledgment of humanity" of the slaves. These provisions and the provision slaves be treated humanely was actually enshrined in the state's Constitution of 1845.

There were, too, various cases in larger slaveholding counties that did result in some slaves winning freedom (this one is among the more famous), and there were also isolated civil suits related to ill-treatment of slaves.

While slaves occasionally got a fair shake in the judicial system, there wasn't an organized abolitionist movement in the state, and little documentation exists that most people came to believe slavery was "wrong." They may have believed it would cause conflict, etc., but it wasn't viewed as wrong. Remember that the inferiority of black slaves was a biblically, religiously-grounded and justified concept in the South, including in Texas.

After the period you seek information on, missionaries of the Methodist Episcopal Church (north) did find some followers in Texas, but they were few and far between. One such minister was actually blamed for various slave troubles, and chased when he left the state, killed, brought back, and his bones ultimately became the playthings of local children on the street.

Texas was not a friendly place to any such changing attitudes on slavery. Hopefully historians with familiarity with other states can provide more detail for you.

SOURCES:

“A Letter from General Cass In Relation to the War and The Ailment Proviso,” The Texas Union, January 29, 1848 (originally printed in the Washington Union, and was dated at Washington, Dec. 21, 1847, and was addressed to A.O. P. Nicholson, of Nashville, Tennessee.) [Via Newsbank Texas Historic Newspapers]

"Abolition," Handbook of Texas (here).

Campbell, Randolph. "An Empire for Slavery: The Peculiar Institution in Texas, 1821–1865," LSU Press, 1991.

"Slavery," Handbook of Texas (here) Dr. Campbell who wrote "Empire for Slavery," wrote this and the following articles for the Handbook, or contributed to them.

"Antebellum Texas," Handbook of Texas (here)

"Texas Troubles," Handbook of Texas (here)

"Anthony Bewley," Handbook of Texas (here)