I agree with you on installing over asphalt.
Where I differ from your opinion is Identifying the slate is most important.
I am in no way an authority on slate.
In recent readings and from specialist that identifying is very important.
If I can learn to identify the type it will go a long way in assisting my client.
I think I have inspected about 6 slate roofs so far. It looks like there are about 8 types of slate. I know it is hard for anyone looking at these photos as they are lousy.
It looks like the life expectancy of this roof is 100-150 years. I believe the problem is when the owner inquires he seeks just a roofer and not a slate roof specialist who would repair and restore the slate and flashings.
I do value you opinion