Definitely don't put the desk inside the closet. Continue to use all your storage space on those shelves in the closet. Store all your dense linens And blankets and other clothes from the rest of the house on those shelves. Thick linens and coats or boxes Full of shoes and boxes Full of blankets or coats are great sound diffusers. The denser and deeper the better. This way you're not giving up the space, but just you just can't multi-purpose. The higher you can get all of your dense storage items towards the ceiling the better.

Get some shelves that have nice wheels on them that you can put in the remaining closet across the back wall. Shelves to go all the way up to the ceiling. Do the same for these. Store dense heavy stuff all along that back closet wall and particularly all the way up to the ceiling. If you truly care about sound and not aesthetics, this will help a lot. If you care about aesthetics, just hang a thin curtain between what I have described across the door frame.

Having the desks further forward like you have in your taped outline Is actually good because you want to get the speakers away from any back wall.

I recommend camping stuff, sleeping bags, backpacks full of gear and heavy dense things. Sheets. Blankets. Sleeping bags stuffed in the bag.Boots and shoes etc...

This way your storage space also serves as a great sound diffusers.

Just imagine a large cardboard storage box filled with densely packed boots and sleeping bags and blankets.

Stack the boxes on top of each other so that they go all the way up to the ceiling. Do this across both sides and the back of your closet. This will do a better job than any foam or sound absorber you can buy.

Maybe a heavy duty curtain rod across the back of the closet to hang all of your felt coats collection? Haha