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OK, our easy method failed to produce a useable texture map, but you can still use the previous lighting and model setup. You can use your previous scene for the second method.

Now, it's time to set up the scene for a cylindrical map.

Create free camera, and set the rendering dimensions to 512 tall (or higher if you need). Change the width of the rendered image to 5 x 512. Make the width an odd number since you will be cropping the image to one pixel. Enable safe frame in the camera viewport. Then modify the viewing angle of the camera until the entire object fits within the vertical frame of the camera viewport. If you have an odd shaped object where you can't see the full extent of the object in the first test render image, then create a cylinder and fit it to the extents of the object.

Create a dummy, and center it to the hi poly object. Use the align button to snap it to the center axis of the object. Link the camera to it.

Set animation length to 1440 total frames.

Animate the dummy so that it rotates the camera around the hi poly object.

Move the last animation key one frame beyond the last frame count. This is to prevent a duplicated column at the beginning and end of the image.

Create a new folder, in the project folder, then make another subfolder. You will render all images to the last subfolder. Nothing must be placed in this folder except for the texture renders.

Render the scene by 1 frame steps.

You will end up with 1440 images. Make sure you delete any test renders. These will not have a number extension. For example, delete face.jpg, and leave face000.jpg.
Create a new image in photoshop, 1440 wide by the height of your rendered image. In this case, it is 512 tall. Make sure you save it to a folder that is separate from the rendered animation folder. Otherwise the batch script will apply the edits to this image.

Open the first image of your rendered image (ie face000.jpg).

Create an Action in Photoshop, then begin recording. Crop the image by altering the canvas size to 1 pixel wide. Leave the height alone. Select all, copy to clipboard. MAKE SURE YOU CLOSE THE IMAGE BY GOING TO FILE>>CLOSE (do not click on the little x button in the corner). After you close thelast image, the large texture image will be active. Just do an Edit>>Paste. Your 1 pixel wide render is now in the middle of your texture image.

Go to Layer>>Flatten image, then go to Filter>>Other and offset by -1 horizontally. Make sure "wrap" is checked. Save the image, then stop the recording.

Go to File>Automate>Batch to start the script.

After the batch automation is complete you may need to change the dimensions of the image for use in your game engine.

Your texture map should look like the image below. As you can see, there are no strangeartifacts, and the stairstepping is minimal compared to other methods.

All you need to do now is apply this map to your low polygon model.
Resulting texture map after batch processing in Photoshop.
Comparison between the original model and low polygon model.