The main concern has been how to pin the circle base to the cylinder body so it will fit neatly. Before I proceed, it is my assumption that: 1) the required seam allowance for the cylinder was followed strictly, and 2) the circle base diameter was correctly obtained using the formula in the eBook.
Why does the circumference of the circle base seem bigger than it should be?
The answer is...because it really should. The unsewn circle base includes the seam allowance, therefore, it's circumference is slightly bigger than the circumference of the already sewn cylinder.
When aligning the circle base to the cylinder, do not attempt to pin together along the edges because it will not work. What you should be aligning to the cylinder is the (imaginary) stitching line, as shown in the photo above. To do this, press the edges together, push the center of the circle in and pin where the stitching line would be. You may not find the exact fit immediately but as you adjust the pins, it should end up fitting correctly.
After you have sewn the pieces together, you will see (as in the photo below) that the circle base is pushed in. The final circumference of this circle is now exactly the same as the body of the carrier.
When you turn the bag to its right side, you should have a nice circle bottom with no tucks (or if there is any, it shouldn't be noticeable).
I don't know if my explanation was clear enough, but again, with accurate seam allowances and correct circle diameter, you shouldn't have any more problems.
Let me know how it works out for you.