I respect the theorycrafting, but this feels like a solution in search of a problem. If Nick wanted to search Vinny's old room, why pick the night of the party to do it? That's the one time people actually go into the room. The place is empty the rest of the time because it's a complete sty. So he could have gone during the week and searched to his heart's content; if anyone bothers to ask him why he's there, he can say he was feeling nostalgic for Vinny.
In addition, if the mansion was 'wrecked' to hide Vinny ransacking the place... why didn't he find the box? Presumably he wouldn't waste time painting alphas everywhere until after he actually found what he was looking for, no? And wrecking the place must have taken a while since it was pretty thorough (aside from Nick's room, which ironically was the one place the damage was merely cosmetic).
Lastly, if both of those attempts failed to locate the puzzle box, why did they stop looking? Surely the next logical move would be for Nick to volunteer to help the MC clean his new room. It would be the ideal opportunity, and again if anyone bothered to wonder why, Nick could always use nostalgia as a cover. As an added bonus, there's good odds the MC would have given Nick the box outright if he asked for it, or even reminisced over Vinny having it.
Now I'll grant you that I might just be thinking about this more than DPC did; he does sometimes cheat to get the story where he wants it to be. But for now I'm inclined to think this theory is a bit too convoluted to be viable. It explains the actions we see, but not why we see those actions instead of other, more logical ones.