I thought of ways to workaround the problem:
- what if I could get my phone to use y.y.y.y in addition to x.x.x.x and
- what if AirDroid was listening on 0.0.0.0 (i.e. it would accept any connection to port 8888 on any interface)
I then connected to my company's VPN using OpenVPN Connect (which was already installed), and that made my phone have the IP address y.y.y.y, and I was able to ping that IP address from my computer.
I then went to http://y.y.y.y:8888 on my computer and it worked perfectly.
Might be too much work for the average user... but I only needed to remove about 8GB of stuff from my phone one time.