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(This is in response to Gerhard Paseman's answer.)

                 .0001            .001 
maxC/M           2.528183          2.528183 
calculated s     4.459300          8.917000 
total error      2.703720          2.718460

The above represents two runs - one incrementing by .0001 and the other .001 (from 0 to 20 in both cases). One trend is that the difference in total error between .001 and .0001 is absolutely consistent with the above, regardless of the data. The total error is in this case divided between 6 elements, each element averaging about 200 in size. If maxC/M were used as s, the total error would have been something like 7 or higher.)

But as to your observation regarding maxC/M being a good starting point for finding s, you can see above what s turned out to be. When using .001 as the increment, s was often much higher than with .0001, (with a consistent reduction in the size of the values for t). So maybe with increasing precision in the search, s converges towards the vicinity of maxC/m, but the example below above has thus far seemed to be fairly typical. Haven't completely digested your remarks above yet. Thanks for letting a non-mathematician like me crash the party here.
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(This is in response to Gerhard Paseman's answer.)

                 .0001            .001 
maxC/M           2.528183          2.528183 
calculated s     4.459300          8.917000 
total error      2.703720          2.718460

The above represents two runs - one incrementing by .0001 and the other .001 (from 0 to 20 in both cases). One trend is that the difference in total error between .001 and .0001 is absolutely consistent with the above, regardless of the data. The total error is in this case divided between 6 elements, each element averaging about 200 in size. If maxC/M were used as s, the total error would have been something like 7 or higher.)

But as to your observation regarding maxC/M being a good starting point for finding s, you can see above what s turned out to be. When using .001 as the increment, s was often much higher than with .0001, (with a consistent reduction in the size of the values for t). So maybe with increasing precision in the search, s converges towards the vicinity of maxC/m, but the example below has thus far seemed to be fairly typical. Haven't completely digested your remarks above yet. Thanks for letting a non-mathematician like me crash the party here.