Lee, you'll need to do your calculations manually. You can't rely on Tableau's auto-totalling function to get the answer you want.
It's a little tricky but that's the only way I can see to get what you want.
Is the format of the display what you want to have in the end? Column subtotals by Region and Grand Totals for every row?
I'm afraid it is. I know this is very Excelish, but this type of table is needed in the analysis we are doing.
Take a look here: displaying average and grand total
And finally on Jonathan Drummey's personal blog (which you should have bookmarked!): Customizing Grand Totals – Part 1 | Drawing with Numbers
This is not an easy question, I'm sorry to say.
Thank you Michael for your input. Talk about being taken "out of the "flow" to come up with what should be a simple thing to do. I was hoping I had overlooked something as some of the links you referenced I found too, but they were so old I had hoped there is something better the last 1 - 5 years. Oh well. Time to roll up my sleeves just to compute an average....