"One way to improve the safety of the installation but at a fraction of
the effort is to install GFI's and label them "no equipment ground";
which was allowable under previous codes but I'm not sure about
current code."


Amen!

ASSuming the GFCI functions, you get more protection against shock with the
GFCI without ground than from a properly grounded outlet.

The "shock" comes from the person being grounded by some other means (e.g.:
by placing a hand on a radiator or sitting in a bath tub) and then touching
a metal object that has been entergized by a cross between "frame" and the
hot wire.

What the proper ground "buys" you is that the GFCI will 'trip' as soon as
you plug in the faulty 3 pin appliance. Without the ground, the GFCI will
only trip when your soft body makes a connection between frame and "real"
ground.

A proper ground without the GFCI should trip the breaker if there is a fault
in th 3 pin appliance.