This morning, I simply did what the artist-e-mail-author suggested and it worked! (Not quoting her, but I'll type the steps I took while doing it again from memory). These instructions (and commentary) explain how to Pattern-Fill the top, side, and front of a box drawn in perspective, and these parts of the box begin as Painter Shapes:

NOTE: My box's top, side, and front were each made from a Rectangular Shape. I used the Shape Selection tool to move each of the four corners and turn the rectangle into a perspective plane. This was the quickest method and quite easy. Before you begin, since you're working with Shapes, be aware that each Shape is listed in the Objects palette, Layers section. Be sure to highlight the Shape you're going to work on before beginning to pick the 4 perspective points and fill the Shape. 

1.Select the Pattern.

2.ChoosePen brush, Pattern Pen variant.

3. In the Brush Controls palette, Cloning section, click Clone Color
box, and Obey Source Selection box, then from the dropdown list, choose
Perspective (4).

4. Make sure that Clone Color is also checked in the Art Materials Color Picker section. It may be that when this box is checked, the settings in Step 3 are automatically made. I haven't checked to see, but in any case both Steps 3 and4will get things set up right.

NOTE: The Pattern tile's 4 points are already, automatically defined: top left is 1, top right is 2, lower right is 3, lower left is 4.

5.Click the BRUSH tool, hold down the Ctrl-Shift keys, and click in the destination image to define the perspective points in the same rotation as you want the Pattern to "lie down" on the surface.

I chose the top of my perspective box as the first section to Fill, and to make the Pattern "lie down" in the right direction. I clicked the far upper right corner first, then the far lower right corner, then the near lower left corner and last, the near upper left corner. Take a look at the image to see where these points are located and understand why I picked the points in that order, remembering the Pattern tile points' position is already automatically set. 

NOTE: Read the NOTE: between Steps 4 and 5 and imagine turning that Pattern tile rectangle to lie down on the box top. Where would each of the Pattern tile's 4 points have to be when you have the Pattern tile positioned as you want the Pattern-Filled image to look? That will tell you where to place the 4 points in the destination image.  The example below is only one position that could be chosen. For instance, the text Pattern tile point's position could be rotated counterclockwise so that the Filled text would be read from the right instead of from the left as it's shown below.

7.Repeat the same Steps as above to define the destination area for the side of the box.

Since the 4 points for the top of the box displayed while I was attempting to define the 4 points for the side of the box, I had to click outside the area I wanted to define, then, while still holding down the Ctrl-Shift keys, I clicked and dragged, one at a time, on the 4 points until they were positioned exactly at the four corners of the box's side. (For the side of the box, I put the first perspective point at the far upper right, second at the far lower right, third at the near lower left, and fourth at the near upper left.)

8.Choose another Pattern to fill the side of the box.

9.Click the Paint Bucket tool, and when asked if you want to Commit the Shape to an Image Layer, click the Commit button, then click the destination image within the defined perspective points.

10.For the front of the box, hold down the Ctrl-Shift keys and put the first perspective point in the upper left, second in the upper right, third in the lower right, and fourth in the lower left. If necessary, click and drag the perspective points to position over the box front corners exactly. 

11.Choose another Pattern to fill the front of the box.

12.Click the Paint Bucket tool, and when asked if you want to Commit the Shape to an Image Layer, click the Commit button, then click the destination image within the defined perspective points for the box's front. 

Now you've finished filling your box planes with Patterns that lie flat on the surfaces and are turned in an appropriate direction for each plane.  I noticed that some of my Pattern Fills seemed to warp a little and not line up exactly with the box surfaces. This may be my lack of experience or it may be something that Painter can't handle precisely. However, with a little practice, it may be possible to compensate for that problem when picking the 4 points, by angling the shape defined by the 4 points just a little in the opposite direction from the warp. 

I hope you enjoy this exercise and go on to do some interesting images using Pattern painting. Let me know how it goes. I'd love to see what you accomplish.