Fiberglass insulation is what they make air filters out of, it isn't the best material for blocking air currents. You need a fire rated stop in the attic, sheet metal as mentioned, or drywall. If you insulate over the top of whatever you put in the attic then there is no need to fill the cavity with insulation. The stash idea is actually a good suggestion as homes accumulate lots of valuables that could be kept out os sight.
The blown in insulations require a machine to fluff it up and blow it in. Big box stores often loan (with a minimum sale) or rent the machines. If they don't have it then check for a specialty business that deals with insulation, maybe (?) they would sell some. But any type of loose fill insulation would work. cellulose would be my choice, but that may be a regional preference.
I really can't see the framing details, but the edges of the sheet metal can be bent up or down to provide a nailing surface if there isn't something. The sell a fire rated caulking to seal the metal to wood.
The suggestion about using something stronger in case you or someone else steps on this area is good. Same caulking and then cover with sheet metal or drywall. 1/2" drywall qualifies.
Bales of insulation that are meant to be blown in are difficult to fluff up, but not impossible. The other method to fill that cavity would be batts or say 6" insulation cur to length and pushed down from the top, or up from the bottom, whichever.
I just don't have the whole picture to guess for other options.
Why would you waste time and money filling the space? You just cover the space on the top, air seal with some canned spray foam, and throw insulation OVER it. Filling that space would be the same as filling an interior room on the second floor with insulation. You don't fill the room, you just insulate the ceiling. So make a ceiling and insulate it.
If it was my house, I'd be extending the closet. Space is too precious to just throw away. My builder thought it was a good idea to build an angled wall in the back of my entry closet. No way was I going to let that fly. I cut a small inspection hole thinking I'd find pipes, ducts, wires... nothing.
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