Interesting. Not much difference in cruise Mach within the extremes of cost index. This suggests to me that the point of least drag is between .83 and .84. My experience on the B777 seems to bear this out as aircraft weight seems to have little to do with it.
Where the big difference occurs between a high and low cost index is in descent profile speeds which due to ATC is out our hands most of the time anyway. Any way of correlating your results to the extent that ATC restricts your speed on descents?
It seems to me that if we could coordinate with ATC to hit an initial arrival fix at a specific time (easy with today's FMC's), that we would be more likely to be able to descend unrestricted which is where some real fuel could be saved. I think that I read somewhere that UPS is trying something like this for their arrivals into their Louiseville hub.