I was thinking that in order to incentivize the most efficient use of one's scrying abilities, and so add to the challenge if desired, particularly once one has improved all their scrying passives, that it would be nice if when one finishes their scrying, that any left over turns of scrying would add to the time you are allotted for Excavation.
In this way one could decide to either just face roll their scrying without caring how many turns it takes (having way more than enough to get the job done), OR they could be more careful and still try to scry with the fewest turns they can in order to maximize excavation time. This would be especially helpful for higher end Antiquities.