Self-Answer from Robert Carter:
To remotely connect to WAS, first, from the WebSphere Integrated Solutions Console:
Navigate to the application server's Debugging Service:
Servers > Server Types > WebSphere application servers > [serverName] > Debugging Service

Check the "Enable service at server startup" checkbox
Add/modify the "JVM debug port" if necessary (the port must not already be in use on the server)
Add/modify the "JVM debug arguments" if necessary (this may already appear by default):
-Xdebug -Xnoagent -Djava.compiler=NONE -Xrunjdwp:transport=dt_socket,server=y,suspend=n,address=7777
Apply the changes, Save the new configuration, and Restart the application server

Then, from the Eclipse IDE:

Open the "Debug" dialog (e.g. Run > Debug Configurations...)
Right-click "Remote Java Application" and select "New"
Configure the Remote Java Application:
Name the debug configuration
Browse to select the project to debug (optional)
Use the "Standard (Socket Attach)" Connection Type
Specify the hostname of your WAS server
Specify the port number that was set in the WAS debug options
Click Apply
Click Debug