Here's a little syntactic sugar to ease the pain:

sub foo {
    my ($self, $arg) = @_;
    &{ $self->{'foo_code'} };
}
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It's still indirect, but as long as you don't shift things out of @_, you don't have to pass $self explicitly. (I can't think of a way to do it otherwise, without actually installing the subroutine in a typeglob in your package somewhere.)