I see from your profile that you're using Monarch 10.5 - so you should be able to solve this problem fairly easily. There is a new feature in Monarch (introduced in v9 or v10) called "User Defined Functions". One of these is designed to handle weekdays and is included in the UserDefinedFunctions.xmod model that you'll find in the standard models folder.
To access it, open your report and model, then go to the Table window. Click on the f(x) icon in the toolbar to call up the UDF dialog. Click on "import" and navigate to UserDefinedFunctions.xmod. You'll see a list of functions and you can import the ones you need into your model. You'll need to import 9 functions - one called "WorkingDays" and eight others prefixed _WorkingDays.
Assuming you've got the UDFs imported into your model, then I would have thought that you could get the answer you need for each day by setting that day, say, Friday, to be the only working day of the week, then getting a count of the number of working days in the interval you need?
If you could email me your report and model to firstname.lastname@example.org[/email] I'll happily have a look.
Just built a model from your sample report, and if you create a lookup field that maps the day letter (F, TH, etc) to numbers (Sunday = 1, Monday = 2 etc), then the UDF gives you the function: CountOccurrencesOfWeekdayInRange(DayNumber,[Start Date],[End Date])
Hopefully that should be just what you need.
F 2010-08-20 2010-10-08 6 7
M 2010-08-16 2010-08-18 2 1
TH 2010-08-17 2010-09-02 5 2
TH 2010-08-17 2010-09-09 5 3
M 2010-08-16 2010-10-13 2 9
W 2010-08-16 2010-10-13 4 8
T 2010-08-17 2010-10-07 3 8
T 2010-10-19 2010-12-07 3 7
M 2010-10-14 2010-12-13 2 8
T 2010-10-14 2010-12-13 3 8
M 2010-11-03 2010-12-13 2 5