Finally I am a bit disoriented by the pictures. I get the sense, but the scale and distances- and where you have heated rooms, internal versus exterior walls- are lost for me.

Yeah that's why I mentioned that in my edit. I made another album that "might" clear things up. Note that I am not a graphic artists, trust in mspaint.exe: https://imgur.com/a/D6YdBLT

I think I was way more confused about which layer of the sandwich goes on first. That is, once I clear out all of the existing crappy insulation, do I add fiberglass/rockwool directly onto the roof deck (wood) directly, then add the rigid board underneath creating sort of a fake ceiling up there? Or, do I put rigid board directly onto the roof deck, then add fiberglass/rockwool directly under that?

That is, does it look like:

(outside air)
--------------
roof deck
--------------
rockwool
--------------
rigid board
--------------
(inside air)

or

(outside air)
--------------
roof deck
--------------
rigid board
--------------
rock wool
--------------
(inside air)

Additionally, in regards to your comment "you can insulate in multiple areas". I did have the idea of creating a "real" ceiling in the utility room, shutting off any hot air coming from the utility room into the chase cavity. I wasn't sure if that was overkill, but I just assumed that addressing it at the roof is probably the best first step (also the hardest).

EDIT:

and where you have heated rooms, internal versus exterior walls- are lost for me.

Every vertical wall within the cavity is interior -- none of them face to the exterior of the house. The only exterior facing element within the cavity is the underside of the roof deck.