from the engine standpoint
We do have some knowledge about volcanic ash and commercial flights. Most notably Mt Pinatuba. Most of the data is known only to the affected airlines and is maintainence related. This data is valuable in deciding how much commercial pressure they can tolerate vs increased maintainence costs.
Examples of these impacts are sand blasting effects on the Fan & compressors, Blockage effects on cooling holes in the turbine and grit in the oil system. None of these maintainence issues have affected the safety of the aircraft (data based) and have been detectable by increased fleet monitoring (costly -yes, but grounding aircraft is worse).
The issues above are airline specific in their decision making.
The safety issues are single flight risks while you are airborne. Thankfully the data is sparse but it does relate to specfic instances that must be avoided or accomodated by altering the aircrafts performance (engines and systems). The idea behind the shutdown of airspace is to minimize such specific issues (you can never eliminate them so you must have procedures at the ready should you encounter them)
Somewhere along the line a decision will be made when it is likely that encountering the severe cases that affect safety of the flight are minimized to something less than the historical data (the Eric Moody type encounters).
I still vote for test flights sooner than later. and a data based risk management approach.