I'm either way with the size 12s...either JR found them and put them on her, or Patsy did. There is no way I'd believe that anyone other than one of them put them on her. We know JonBenet didn't because they were not available to her to be chosen to be worn like Patsy tried to claim. They were NOT in her underwear drawer with all of her other underwear (and all of those in size 4/6) when police were searching the house, no doubt specifically looking for underwear in the same size as the huge ones found on the body. IMO, either the size 12s were never in her underwear drawer to begin with, or someone removed them before police checked underwear drawers for evidence, or both.
I kinda lean towards JR being the one who put the underwear on her, due to the fiber evidence, but I could also see Patsy making sure his fibers were on the underwear as leverage to make him comply and conspire ("I'll tell them you were doing XYZ if you don't go along with this" - I don't think Patsy was that vicious, but I also don't know how desperate she may have been, considering the staging and lying and RN indicate a very high level of desperation to me.)
As far as the gift being obvious as the underwear due to a cydrilical-shaped tube container...what if that container was put into another box before being wrapped, maybe to disguise shape? My family does that a lot - we'll fool the recipient into thinking they've gotten something big because it's in a big box (when it's something small like a new wallet) or we'll put something good, such as a really nice new watch, in a boring box, like one that a cheesy clock radio came in. I'm not saying that's what was going on with the Rs and the bloomies, but it's possible.