The methodology you have identified in Section VIII, Division 2 is also found (and is almost identical) in Code Case 2286-6 which is applicable to Section VIII, Division 1. That Code Case directly addresses column buckling as a potential failure mode.
If you refer to that Code Case, note that the calculation for "lambda c" uses "Lu", where "Lu" is defined as follows:
Lu = laterally unbraced (laterally unsupported) length of a cylindrical member that is subject to column buckling, in. This applies to supports for pressure vessels or pedestal type vessels. Stiffening rings are not points of support unless they are externally supported. (Refer also to additional explanation at the end of this nomenclature section.)
Additional explanation...
In the equation for λc above, a laterally unsupported length, Lu , for a free-standing pressure vessel without guide wires or other bracing should be measured from the top head tangent line to the base of the vessel support skirt. For λc values ≤ 0.15, consideration for column instability (column buckling) is not required for either the vessel shell or the vessel skirt for any of the load combinations in 5. For λc > 0.15, consideration for column buckling is required, see 5 and specifically 5.1.2.
In your response above you identified that Lu is the total unbraced length of the column. In the civil / structural world, they brace beams often and can use a reduced length in their calculations, however, I have seen very few guyed or guided vessels for which you could make the argument that you have a "brace" that would permit you to use a reduced length. Furthermore the type of "bracing" and how the vessel is supported at some midpoint would influence the "K" value (something to remember). Most vessels that I have seen are simply free standing pressure vessels supported at grade, but that may be a function of the industry in which I work.
Also note that you need to determine the radius of gyration in your calculation, which may be difficult if your vessel isn't a continuous diameter with a constant thickness (which usually doesn't happen). The easiest thing to do may be to calculate the least radius of gyration, but this may be overly conservative. I am not certain how commercially available software calculates the radius of gyration if the vessel is not a uniform diameter and thickness, and I do not know if you can override it with a less conservative value, but that may be an option. There are methods for calculating an equivalent radius of gyration, but those methods are not in the Code.
Years ago when the rules for compressive stresses in Division 2 were changed (2007) I saw many supplier calculations that were using the value of "Lu" as the distance between lines of supports (head to head on a skirt supported vessel), the distance from the top of the skirt to the bottom of the skirt (which was treated as a pinned-fixed with K = 0.8), or as the distance between shell courses! The commentary I pasted above is relatively new in the Code Case. I'm thinking they added it to eliminate the confusion of which length you should use. As you noticed the check for column buckling is different than the check for local buckling, so the appropriate length should be used.
At the design stage, you may have an option to increase shell course thickness, flare the skirt, or do anything to increase the radius of gyration, since guiding the vessel not commonly done (in my experience). If you are beyond the limits for lambdac in using the Code Case, you will have to fall back on U-2(g).
Edit - Years ago a KL/r limit of 200 was maintained, which was an old rule of thumb that is even listed in Code Case 2286, Section 3.2.2 as being an upper bound for that section.
Hope this helps.
