Sorry.

There's probably a lot of ways to do this, but I would create a
"whoami" web service (see other posts) and add a readonly field with
the label "Last Modified By".

Then I would go into Tools/Form Options/Open and Save and check the
"Save Using Custom Code" box, edit the code and add a line that
assigned the field's value to the whoami result immediately before the
form is saved.

But on second thought, I guess it would be better to create a rule
that assigned the fields value when the form was opened (also in
Tools/Form Options/Open and Save). This way, the user would see that
their name was on the form as the last modifier. Shucks. Downside is
that if a user opens the form, they'll see their name whether or not
they've made a change to it.  If they don't save it, the field keeps
its original value.

Nah.

FWIW, in the situation you describe I would also be making heavy use
of user roles and assigning views appropriate to those roles. For
instance, the form defaults to a read only view and when the user
changes it to a view that allows modification, *then* set the "last
modified by" field.

Choices, choices. :)