Is there an easy way to override DBI::prepare or 'execute' in such a way that I can add some logging to give a stack trace (Carp::cluck) showing where every database query in a large body of code was called from, as it runs?

Assuming that you control the code that's doing the prepare(), a simple approach is to wrap the object that prepare() hands back. Something like:

    my $sth = $dbh->prepare("SELECT ... WHERE ... ? ...");
    $sth = Statement->wrap($sth, "Label");
    ...
    $sth->execute(@args);
[download]

The wrapping class looks something like:

    package Statement;

    sub wrap {
        my($pkg, $sth, $label) = @_;
        bless [ $sth, $label ], $pkg;
    }

    sub execute {
        my $self = shift;
        # tracing, timing code here. E.g.,
        log($self->[1] . " is about to execute");
        my $rv = $self->[0]->execute(@args);
        # timing, logging code here
    }

    sub finish {
        my $self = shift;
        $self->[0]->finish();
    }

    1;
[download]

You'll probably find that you need to wrap some additional methods.

The label helps track the statement and makes the logs more readable, and could include the text of the query.