The "upward spike" in tariff rates is due first to the withdrawal of Southern Senators and Representatives from Congress and secondly to the necessity of financing the war. Higher taxes, North and South, were the rule during the war.
Do they mention the support of James Buchanan and other Democrats for an upward revision of tariffs to pay for the deficit? Regardless of what we think about the economic wisdom of this, a modest increase in tariff rates was apparently a relatively uncontroversial proposal in the early Buchanan administration.
Do they mention sugar tariffs? It's been alleged that the Confederacy retained the protective sugar tariff to please Louisiana. If true, it's a blow to the views attributed to the article's authors and to their whole reading of the Confederate Constitution.
And of course, an area under blockade was not likely to get much from import tariffs. One would have to consider other taxes as well, such as the income tax, capital levies, labor requisitions, excise taxes, the export tax, and the "hidden tax" of inflation. Military needs led the Confederate government to establish a highly centralized and bureaucratized comparatively high-tax wartime regime. There may be some truth in a snapshot view of Confederate attitudes towards tariffs in 1861, but since we don't know what tax policies the Confederacy would eventually have pursued, it's hard to make a comparison to subsequent US tax history.
Given that a revolt against higher taxes led to the nation's founding, it would be surprising if no one in 19th century America argued that lower taxes would stimulate economic activity. But what distinguished Jefferson Davis's South from Ronald Reagan's America is the largely colonial character of region. Lower import duties might bring some economic stimulation, but would not necessarily promote the development of industry or economic independence. Low tariffs promoted an agrarian economy that was dependent on foreign markets for its raw materials. It was natural that those who weren't a part of this colonial arrangement would be economically marginalized and wish for industrial stimulation.
Ronald Reagan's America already had a highly trained workforce, a comprehensive transportation network, and a developed industrial and commercial infrastructure. The fear in the mid-nineteenth century was that an America which devoted itself to providing raw materials for foreign manufacturers would never have developed such institutions. To some degree this became a North vs. South issue, but the development of industry clearly would have benefited poor Southern Whites and however many or few free Blacks as lived there. It would also have had national or regional defense benefits. But it conflicted with the slave-based, export crop economy and the power of the dominant class.
That's not to say that the low tariff side was wrong or that industrial development was a wholly good thing. Many of us would have preferred an agrarian country, if that option hadn't been bundled with slavery. I just point out that 1861 was not 1981, and the context surrounding tax and tariff questions was very different for Davis and Reagan. To ignore the colonial elements in the Southern economy of the day is to leave something very important out of the picture.
Actually with representatives, no. The southern representatives were all there when the Morrill bill was voted on in May 1860. All but one of them voted against it, whereas all but some 5-6 yankees voted for it.
Do they mention the support of James Buchanan and other Democrats for an upward revision of tariffs to pay for the deficit?
They do mention the northern Democrats support of it as a sectional thing, as well as the southern one's opposition. They also look at the rates some and point out it's schedule contained revenue measures but also protection measures, found in the higher end rates of the schedule.
a modest increase in tariff rates
The problem is it was not modest at all. They literally doubled the rates from 1861, which had been the low rates in place from the late 1850's, to 1862 after the Morrill bill. The average rates went from 18% to 36%.
was apparently a relatively uncontroversial proposal
All indications are that it was anything but and drew sharp sectional opposition from the south in near unanimaty.