You were on the right track, but the problem is that in this case both average and stdev are properties of the whole sample, while Tableau automatically uses only what is inside a cell for calculations. If your imagine a table behind your graph, then your forumlae will calculate AVG and STDEV for each cell of the table, not the whole table; but you need the whole table.
In other words, you should have used table calculations for average and St.Dev, i.e.
WINDOW_AVG(...) and WINDOW_STDEV(...)
See attached workbook for the solution (I had to remove the filter to match the numbers in your post).
Worked like a charm . . . but i'm sure you knew that. Thanks so much!