Here is the result I achieved using your images (I slightly cropped the decal to eliminate the white border around it):
The XCF file can be downloaded from the following webpage:
http://barn.kerosenecow.net/u/saul/m/michelin-xcf-d7d2/Before starting, I first scaled the tire image so that the tire was 139mm in diameter at 300 DPI.
I then created a selection around the outer circumference of the "whitewall" and noted it was 1526 pixels in diameter. I then created a selection around the inner circumference and measured the thickness of the "whitewall" to be 91 pixels.
I scaled the decal image to be 1103x182 pixels (actually I just changed the height, the width of 1103 was automatically calculated to maintain the same aspect ratio).
Next I resized the canvas of the decal to be 9198x1526 pixels (again, the width was automatically calculated by GIMP based on a height of 1526 and a constant aspect ratio).
Next, I added an alpha channel to the decal layer and performed a "Layer->Layer to Image Size".
I then performed the Polar Coordinates operation, using an offset angle of 180 and unchecking the Map From Top option.
Finally, I autocropped the layer (resulting in a layer that was 562x139px).
The resulting decal layer was copied to the tire image to verify that it fit.
If done properly, the decal layer should be able to be added to a letter-sized image and printed on a 300DPI printer.