Hi Cool Aid
To answer the easy questions...
Yes it is true that the customer transaction listing for a month should tie to the net change in the GL control account for the month. The key word here is "should".
The same should be true for the net change between any two period ends, including a whole fiscal year, assuming you are keeping history in AR for that period.
You are correct that the original amount is the amount to use for purposes of this exercise.
Now for the hard question...
Why reality doesn't match theory can be due to a whole slew of reasons. The first thing to check is whether the GL control account balance agrees to the aged trial balance as of the two period ends. If it does, then it should be fairly straightforward to reconcile any differences by exporting both reports to Excel and matching. If it doesn't, user error is the most likely (but not only) cause, and troubleshooting this is beyond the scope of a first reply on this forum.
Steve