My view on the story of DiPP, putting aside DiPP's lack of relevance canon-wise :
Let's sum thing up a bit :
Curious one : seems like he was going to be handed the jewelled branch of hourai, died
Earliest riser : sees shrine maiden dancing, shrine maidens eventually disappears, rain falls
Beautiful one : rain becomes storm, went away with the pierrot, not mentionned if dead
Youngest one : snuck away from the party, died
Cowardly one : ran away, he wasn't expecting to see his loved one anymore, hanged himself, didn't die, says he was reborn & still going to pretend to be human
Wisest one : the group has been captured by the pierrot, the 4 others planned to escape and succeded, died like a dumb dumb
Remaining 4 : escaped into an western style building in the forest
Most mature one : drink his tea which seemed to taste different from usual, died, falling in love with a beautiful clown
Most wary one : heard noises of a spike being pounded into a tree, then realised later he was nailed to the tree, died
Earliest riser : on his last moments after eating suspicious food, dies
The one who was reborn : hang himself again
Various comments regarding the soundtrack themselves were put aside, cuz it's not certain if they are relevant to the story or not, and may only add confusion
So, basically, It's the story of a bunch of "honest men" who were formerly thieves trying to start a new life in a paradise-like place, but they get picked of one by one by a suspicious pierrot
The number of honest men still decreases when the beautiful one goes away with the pierrot, despite there being no mention off them getting killed by the pierrot or not
But putting that aside, here's the thing : all of the stories seems to be told from the point of view of whoever is experiencing them, until they die anyway, and they're expected to be true because they're being told by honest people ... but by the end, it becomes quite clear that the pierrot, who killed everbody, was part of the group to begin with ... in other words, one person is not honest, and one story is therefore probably wrong, a lie. The story of the beautiful one sticks out as it is not mentionned that the beautiful one was killed or not, just that they went away with the pierrot ... but what if this was the lie and the beautiful one did not go with the pierrot but was the pierrot and just went away from the group before picking them off ? Latet in the story, the earliest riser mention that one of them should have killed X when they went mad ... if X was the beautiful one and was indeed mad, then their story about going away with the pierrot holds no credibility whatsoever ... long thing short, the beautiful one's story is a lie, and the beautiful one is the pierrot.
About the beautiful one ... in his last moments, the earliest riser asks himself if she was always this blonde. By this point everyone's gender is uncertain, and there is an assumption that he was refering to the shrine maiden since he was reminiscing of her quite a bit before (to which I disagree for the following reason), and the shrine maiden herself notes in her diary that from the neglected western-style mansion in located in the forest came out a beautiful blonde girl, and that from the group of 8 honest men, 1 was actually a girl. So what I'm saying is that aside from being the pierrot, the beautiful one is the blonde lady that the earliest riser saw in his last moments.
So we have this beautiful blonde girl who came out from a neglected western-style mansion located in the forest, who seemed to have been compared to a doll at one point, and having killed someone with some kind of voodoo technique at another point ... that's like the perfect profile for Alice Margatroid ...
A few additionnal point could be added to further conciliate Alice Margatroid and the beautiful one, for example their familiarity with outside world stuff, as the beautiful one's "friends" (and herself since she's part of the group) as they would have tea and eat not-so japanese food such as eggs and ham, while Alice's dolls seems to be named after outside world locations. There is also the regular mention or even the presence of a hanged doll by Alice's side, quite reminiscent of the cowardly one / the one who was reborn's end : as the only honest man who wasn't killed by the pierrot (and probably even saved from the first hanging), maybe there's a certain sense of fondness for this one or something ? And there is also Alice being quite comfortble around Marisa, who is a thief (quite a prevalent part of the setting back in the time)
Now, the album being from 2002, which was a time where ZUN would say that "Touhou is not a series" and where Touhou still had a bunch of PC-98 influences (rank system, Sakuya, Alice (duh) & her Reimu dialogue, PCB extra stages final sections, Yuuka), it is not unconceivable that ZUN would feature a tie-in or a shout out to PC-98 stuff. Alice and Reimu's dialogue from PCB from exemple (the trial of which probably came around close to PiDD's being released) indicates that ZUN had a particular setting for Alice in ming ... and since we're talking about PC-98 influence, I suspect that even back at the time, the "exit of paradise" that the beautiful one was moving towards to was not actually someplace that lead to the outside world (which also seemed absolutely impossible to reach at least before modern touhou stuff like 14.5), but probably Makai for example ... (although it may not necessarily make sense chronology wise)
So yeah, long thing short, Alice is probably the beautiful one, and PiDD story may probaby be used to deduce a backstory of sort for her, if you stretch it quite a bit ... the more bizarre / confusing part for me would be the cowardly one / the one who is reborn parts
But at any rate, this is a story I would not take super seriously, speculations aside : there are a bunch of stuff from far back in the past that you can see now, but a self-containing story that was never expanded upon, received mention further down the line, or had any relevance in current or not-so current touhou cannon is definitely not something I'd put on the same level as stuff like the Hifuu club stories or any other official book. A bizarre and curious story DiPP is, but for something super old from 2002, probably irrelevant to canon.