I don’t realistically see this happening, but I agree it’s worthwhile to say and to think about. I assumed any change we made could be instantly undone by a hostile ASI, but you raise an interesting point; relying on a hard speed-of-light limit seems like it could be our best shot at a legitimate counter, so far as it goes.
The question of what information could or should be transmitted seems likely to be contentious, however. Even provided we gain the ability to do it before it becomes moot, broadcasting information sufficient to reconstitute ourselves or something similar strikes me as yet another big roll of the dice. This is particularly true given that we can’t know in advance whether or not we’re bound for an ASI failure mode, and as soon as we do, it’s presumably too late.
As of about ten years ago, gravitational waves are no longer theoretical. That said, I think that given the profound relative weakness of gravitational force, the technology to be able to generate waves is far out of reach; naively, I’d expect we’d have to be able to wiggle multiple-stellar-mass objects around in a controlled way.