Also, if you can find their outer-system presence you can post your diplo ship near a fuel extractor site or something where the aliens hang out but don't have vigorous territorial interests. That should cut back on the damage control.
(Meanwhile, I've been simultaneously pestering mine with stealth ELINT ships that sneak around in their homeworld's orbit taking notes. They get caught occasionally, but only occasionally, and they look fighter-sized because of the cloaking...