I finally got a proper monitor stand. It was on sale, and came with a laptop attachment, which was a bonus at the time but I've really grown to appreciate.
The amount of space this has returned to me, by removing the base of the monitor and the books previously holding up the laptop, was surprisingly large. Now I feel like I'm never without room.
Luckily, I found a place to put the webcam - mounted on a thin metal rod that I've inserted into the hollow monitor stand.