So, I finally seem to have gotten around to discovering the problem with my N5.
Apparently, there is a conflict between the script below, reported in this and other forums, and Morph Browser. The script is used to increase the overall font size displayed on the phone. It's very useful, since at the moment there is no way to increase the size of the GUI fonts, which are very small to read—at least for me, they are.
The script is called gu.conf, and is placed in /home/phablet/.config/upstart/gu.conf
This is its content. The pixel number can be changed at leisure.
start on starting dbus
exec initctl set-env --global GRID_UNIT_PX=27
It looks like that the variable set here doesn't go down too well with Morph Browser.
Removing or commenting out the script restores the functionality to Morph Browser.
That's all I found.