Using the drywall to carry the weight of anything like AV equipment is asking for a disaster.
You probably need to cover the back of the nitch with 1.2 inch plywood fastened to framing to take the load at the rear of the shelf.
I have made a number of shelves that have no visible support. The method is to fasten a ledger to he wall (or walls) and then build a torsion box (plywood top and bottom with a grid of smaller lumber inside) that slides overthe ledger board. If the torsion box is made strong enough it can support a large load (a person sittnig on the shelf) but the ledger must be fastened to studs using lag screws to prevent pull out.

wait a minnit--how heavy is an audio-visual receiver? Not THAT heavy, is it?

I don't think you need to add the plywood (which will eat up 1.5 inches of space!) for this--I think that's overkill.

If you give EACH piece of equipment its OWN shelf, and don't stack them up, how much are you holding? My receiver isn't that heavy. Can you weigh yours?

They make drywall anchors rated for some pretty big poundage--they ought to work just fine. Round way up, for safety's sake.

And, as I mentioned, don't stack them all on a single shelf. If you want to pass wires from top to bottom in the back, get a hole saw, and cut a hole through the back of the shelf.

Esp. coupled w/ the front being screwed right into the studs, they shouldn't fail.

If you're worried anyway, or if you think that TOO many holes will weaken its holding power, you might just put a 2x2 in each corner, and attach to floor and ceiling, so it doesn't wobble; if this is *sitting* on the floor, and shelves are anchored to it, they'll stay up.

(also, most of what you do in the back can be hidden again by the shelves themselves; you could try to access the drywall that frames the niche, even if it's messy)

You don't need support across the back, not w/ 18" wide, at 3/4 inch. It won't sag. Just support at the corners. (or the back wall itself, IN the corners--is there NO framing accessible in the back at ALL? The drywall itself has to be attached to SOMETHING)

For the shelves, you could just get plywood cut to fit (trim the front edge w/ iron-on edge banding, ask at the lumberyard).

To hold it up, set it on either 2-inch metal L brackets (upside down).

Of course, the L brackets will be pretty low profile, but they will show. I wonder if you could simply set them on the screws (use extra-long ones, so they'll stick out a bit AFTER they've gone all the way through the drywall anchor). If you don't leave TOO much sticking out--just enough to grab--maybe they won't bend.

If you use the screws, and have a router, you could gouge a tiny notch in the bottom of the shelf (use a thicker board, then) for the screw to sink into. Maybe there's a bolt w/a screw end you could use--you might ask at the hardware store.