With earthworks, unless you know the exact details of the soil or machinery masses, number of passes, etc you cannot report on the exact quantity in the pile.
I once worked for a survey firm that did stockpile volumes and waste heap volumes for mining companies. The mining company and their earthmoving contractor both agreed that the as placed volume was sufficient for contract payments. The contractor had allowed for approximate compaction, soil properties, etc in his contract rates.
The best thing to do is report the quantity in terms of volume occupied by the pile (as done), don't get involved in estimating masses or compaction as there are too many unknowns. Also it is worth placing a disclaimer on the volume report that the quantity calculated is not 100% accurate due to limitations in survey and calculations methods.
What is the reason that you wish to refine the volume for?
Regards
sc