Thanks for your (general) answer.
My questions were quite specific, mostly because it seemed to me on available evidence (in the case of the airlines, actually very little!) that the existing volcanic ash diagnostics were probably not quick and possibly not effective. Note that ALL the reportage and also operational pilots' comments I've seen on the technical aspects of ash investigation have focused on only two things: external, physical checks and borescoping. The first seems to be ineffective with respect to ash (see NASA report I referenced) and the second is certainly not going to be quick!
I'm entirely with you are on the key difference between catastrophic IFSDs as a result of flying through dense ash and the much more costly (!!) long-term impact via increased costs for post-flight checks AND turbine maintenance on the far greater number of aircraft affected by much lower ash densities.
If it turns out that the other parties (Met Office, ...?) CANNOT provide sufficiently detailed volcanic ash forecasts including both location AND particle characteristics AND ppm in the intake air, as seems to be the case right now, it's down to you guys to run the best diagnostics and then do the required maintenance on the correct aircraft.
First-line investigation using long-winded methods (borescoping?) on the apron is not a realistic option. That was my motivation for asking about filter analysis - simple questions for which I hoped there'd be simple answers.