I've found the problem and a workaround for my own machine but would really appreciate advice on a better way to handle this for distribution to other users.
The problem is that there is a KillBit set for the web browser object due to a security issue.
The workaround (which presumably leaves the user open to the security issue) is to go into the registry and change the value from 400 to 0. The address for my 64 bit system is:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Office\15.0\Common\COM Compatibility\{8856F961-340A-11D0-A96B-00C04FD705A2}
but if you search for "COM Compatibility" you should find the right place.
After closing and restarting Excel the web browsers appeared and function as expected.