If I read this right then the worst case scenario is rebuilding the detectors from scratch.
That might be an excellent end of life project for the LHC.
In the interim another classic solution to this kind of problem is simply randomise the sampling process.
By that I mean if we are not sure that the thresholds for these triggers are optimal is it possible to automatically explore all possible trigger parameters? In this case the null hypothesis results would be quite trivial to derive as the null hypothesis is “no new physics”. We would only have to be a relatively sure we could model the impact of the changed thresholds on the measurement outcomes…