Ok, I really like that, it fits everything I can think of, based on our stated assumpions.
So lets take a step back and examine the other possibility: What if the items were Prepared ahead of time (empowered for Ritual purposes)? Setting aside the question of Who and Why, What would the items have been made to do? Based on the classic story I tend to think that, whomever was behind it, Jesus was aware of it if not an active participant of The Plan, but Im not attached to that.
Each possibility has an unknown factor involved, and Im not sure which is more likely. If they were empowered byt he events themselves, the question is Why those 5/6 items alone got empowered (to that degree at least), while there are other equally famous relics associated with it: the Scourge he was whipped with, the whipping post, The Seamless Coat, the Veil of Veronica in particular (which aurguably fits the theme better than the Shroud). And let's not forget my personal favorite Holy Relic, the Holy Prepuce. But it could all be there in the background/shadows the the DV specific history and we simply havent been made aware of it. But that is the exact same problem with the idea of them being prepared ahead of time: we have to ask Who and Why and How and all of that. It could easily be made to make sense in the DV, but we just dont know yet (or really have anything much to go on).
Well the easiest answer is one of two. Either the Passion, Crucifixion and Resurrection were all a ritual in and of themselves to specifically empower these items, OR the same events of which all these items were involved in is the reason they garnered this power.
I tend to favor something more towards the latter because the event itself is arguably the single most relevant and important set of aspects surrounding Jesus' life. I mean this was supposed to be the whole reason he was born, to die for humanities sins. That kind of attachment has made these items revered worldwide for centuries. All the other items you mention, while some have direct involvement even, I would argue are nowhere near the same top tier level of 'importance' as has been placed on the five bit items plus the nails. And I think since we've already got the in book example of the fake Shroud lending us credence to faith empowering even a useless rag...that it still fits the in book rationale as to why these items specifically mean so much more than the holy foreskin or the Scourge for instance.
Because if I walked up to a random person on the street and asked them what the Seamless Robe was i'd get the glazed over look...but mention the Holy Grail and at a minimum you get a Monty Python quote, but you get my point. So I think its very easy to differentiate which ones really matter even if we're sticking to a strictly 'belief' empowerment theme granted by the importance of the event itself. For myself personally I think the five items chosen in this story are realistically far more well known than that second level you illustrated, even over the few that were directly involved in Passion but weren't in the Vault.
Concurrently when you bring in an idea as you had with the Egyptian example which fit so well to the items, Nails too accepting my rationale, the others (maybe Veil excluded) seem like a stretch at best to fit the themes. And since I liked that theme I think it lends credence to the importance of these items over the others based on 'fame' for lack of a better term as being valid.
As for the idea the items were prepped beforehand, if it turns out to be the case then that's cool too but unlike the Swords which are 'easy' to attribute other version from in history...I have yet to see a real comprehensive list of examples of prior representation for these items as we know them now.