Telling whether the gamma rays arrived at just the right time or not would seem to be really tough. I'm not sure, would need to crunch the numbers.

Short answer: The numbers come out in the ballpark of hours not seconds.

Hmm, what about actively racing them? Same method as yours but closer in.

Being closer in relies on trusting your engineering competence to be able to calibrate your devices well. Do it based off interstellar events and you just need to go "Ok, this telescope went bleep at least a few minutes before that one" then start scribbling down math. I never trust my engineering over my physics.