My "asterisked" * choices show I'm no fan of particularly "exotic" ammunition choices for HD.

Lessee... Yup: All 2-3/4" shells, with recoil reduced loads preferred, No. 4 buckshot for inside, No. 1 buck and good old-fashioned buckshot.

A much shorter list, certainly! As far as the Remington "UHD" loads--which one hopes were discontinued--the idea was to make a dense-for-size (I'm sure you engineers have a snazzy term for what I'm getting at..."denser?") birdshot to cater to the birdshot for HD crowd... That and charge about three or four times more per shell than the demonstrably effective 00 buck on offer for decades.

I tried to include 20-gauge and even 16-gauge because I don't know what type of Rem. 870 is being discussed...
As far as resurrecting the olde-timey "buck and ball" load, I also agree completely. I'm not sure what purpose it serves unless one is, say, defending Bunker Hill from a column of scarlet-clad line infantry on His Majesty's Service to drive upstart "Brother Jonathan" colonists and rustics from the outskirts of Boston... Certainly smoothbores have been loaded that way for military applications in the 18th and 19th centuries...

These days, it appears that while various "multi-shot" sizes have been experimented with, the "go-to" loads have typically been 2-3/4" 9 pellet 00 buckshot. That was the load used in the so-called "Malaya Emergency" where the Brits and Commonwealth squared off against communist MRLA guerrillas in very dense, triple canopy jungle where ambushes were frequent and ranges startlingly short. One of the few combat uses of shotguns, e.g. for "antipersonnel" use that generated a detailed study.
Moving to U.S. police/Law Enforcement and defensive use generates a much, much larger possible "data set" and a similarly narrow set of criteria: 00 buck was renowned as a "fight stopper" during the Prohibition gangster era and the Depression era "motor bandits" using V-8 automobiles alike. Police departments concerned about liability issues and "over penetration" adopted No.4 buck. Complaints about its lack of efficacy in penetrating cover, such as automobile bodies and so on, led to evaluations of No.1 buckshot as something of a "compromise." This, in turn, stimulated a bunch of ghastly "wound ballisticians" to tabulate that the combined surface area of a load of 16 pellet no. 1 buck from a 2-3/4" promised to be even more devastating than the older 00 buck. As you've pointed out, some of those "00" buck pellets are actually "0" aught, so I'm not sure...

Thanks for the critique of the "broad field" of choices! The "choice" is actually much narrower... But on the other hand, the sheer versatility of loads available to the Rem. 870 shotgun user is a very interesting subject.