We just need some definition of how much ash can be suspended in a given quantity of air without becoming a problem.
If that concentration is zero ppm, then so be it. Ops must be suspended until every single ash particle has left the atmosphere.
On the other hand, I suspect a safe limit could be established initially and an ongoing period of careful monitoring of aircraft engines and systems put in place to build a solid knowledge base.
I think the best, in fact the only, way to discover this with any degree of confidence, is to fly.
This ought to commence immediately so that we can quickly ascertain 'safe' ash levels and also to discover if particular models of a/c engine are more susceptible than others.
There may also be other problems, perhaps related to pitot static and other systems.
Again, we can't model this sort of thing. Aircraft will have to fly in it- empty if neccessary.
The data thus gathered will be useful should this sort of thing happen again.