Shortly after posting the above question I posted what I thought was the answer, but it was an incorrect answer and I've since deleted it.
I've experimented with creating a version of the ratio that needs to be averaged across a calculated segment where I divide by window_count() or size() so that each customer only contributes their fractional portion to the composite grand average, but I'm unable to include in the formula the count of the number of people in each of those partitions. I think that's in part because the calculation "purchaser segment" is an aggregate calculation and can't be a dimension.
Anyone either know of an answer or that it is (gasp) impossible?
Here's a solution:
1) Uncheck "Ignore in Table Calculations" on the Purchaser Segment pill. That lets the table calculation partition (restart) for each new Purchaser Segment.
2) Set up a table calc with the formula IF FIRST()==0 THEN WINDOW_AVG(SUM([purchases])) END, and bring it into the view with a Compute Using of the Customer Number. The IF FIRST()==0 ensures that we only return the result once for each partition (the Purchaser Segment) and the WINDOW_AVG() does the right calculation.
I set this up in the attached.
Works perfectly, thanks!