I think you're giving the taper too much power.

If something needs to be in a bin, that bin doesn't need to exactly fill up the whole shelf. Lots of stuff may not need to go in bins or baskets anyway.

You could get 12"-deep boxes and put them on the deeper side, and leave the rest of the shelf for setting things that don't go in bins or boxes.

Or, if you do need a bin that exactly fills the shelf, can't you use your plethora of woodworking tools to make your own in a trapezoidal shape? It's just an oddly shaped wooden drawer, which is itself a lidless wooden box. (I made a storage box/bin for an oddly shaped space by cutting up foam-core board and hot-gluing it together. Now and then I have to reinforce it, but it works great! I'm too lazy to make it out of wood, and I don't have a lot of experience using thinner wood like 1/4" luan or masonite, and 3/4" stock would be too heavy)

You could install shelves, or you could make "pockets" to hang on the wall based on what's going to go in them (if you make your own pockets, you can make them as fat as you need for whatever you're going to put in them).

I'd say:

First, figure out how to put a single hanging rod on the 24"-deep side (and
limit how many coats can go in there--everybody in the family gets two
hangers, and any other outerwear goes in the bedroom). Or, put in one
hanging rod (those Closet-Maid/Elfa wire shelves?) for long coats, and
install second one halfway down the wall to convert one half of that
space for jackets? My experience is that especially in winter, there are
more hip-length coats than short jackets, so plan for winter, not
spring or fall.

Then see what sorts of other storage needs you
can fulfill there--would the vacuum bit on the coats side? Can you put
pockets on the side wall for gloves, hooks for umbrellas and dog
leashes? Can you put a tray or basket on the floor to hold boots or
shoes? Or something on the shelf above the hanging rod that would be
useful for what you store there?

Then stand in front of that tapered side with all the stuff you're going to put in there, and see what inspires you.
Do you want shelves you can put boxes on? (You could make a small trapezoidal bookcase and bolt it to the wall, leaving space below it; or use brackets on the back wall to install tapered shelves--you can buy brackets of varying lengths.)

Would pockets or baskets on the side wall be useful for stuff like cleaning supplies or shoes? Would hooks allow you to use the most shallow section for hanging the vacuum hose?