my $sticky_dir;                                             # EDIT
sub import {
    shift;

    my %names;
    foreach (reverse @_) {
        my $path = $_;          # we'll be modifying it, so break the alias
        $sticky_dir = $path unless $sticky_dir;             # EDIT
        if ($path eq '') {

    ...

    # remove trailing duplicates
    @INC = grep { ++$names{$_} == 1 } @INC;

    # put sticky dir up front                               # EDIT
    @INC = ($sticky_dir, grep { ! m{^$sticky_dir$} } @INC); # EDIT
    return;
}