I just didn't think of coming up with a Perl 6 solution, and even now I don't see a particularly elegant and readable way.

So I've just ported toolic's solution to Perl 6, making the returned list of found values lazy:

my @a = <eval DBIC::3 DBIC::2 DBIC::1 MyApp::3 MyApp::2 MyApp::1 Dance
+r::3 Dancer::2 Dancer::1>;
my @filtered := gather {
    my $flag = 0;
    for @a {
        last if /Dancer/;
        $flag = 1 if /DBIC/;
        $flag = 2 if $flag && !/DBIC/;
        take $_ if $flag == 2;
    }
}
.say for @filtered;
[download]

(Tested with current Niecza)