Dynamic MOD & COLUMNS formula

I sincerely appreciate the effort. However, the data coming back on this is dramatically different than what is coming from the original spreadsheet when I choose a date range that includes all dates. I'll spend some time trying to decipher exactly what your formulas do, and thanks for the effort, but I may just have to manually adjust the formulas in my present sheet to get what I'm looking for. I can probably do it with search & replace. Not very elegant, but feasible.

INDIRECT function did the trick.
{=AVERAGE(IF((INDIRECT($R13)<>"")*(MOD(COLUMN(INDIRECT($R13)),F$3)=F$2),INDIRECT($R13)))}

Where R13 combined the first half of the range name with the second half which represented the date. Manually entering the range names, but way better than it was.