The problem is with the jpgs you are using. Doesn't sound like they tile very well, hence the checkerboard effect. They need to be cropped perfectly so th eapttern matches and you might also have some light to dark lighting variation.
Best thing to do is take some really good pictures of the fabric in a consistant lighting environment. Then crop them so they are tilable. You can do this yourself or higher a professional photographer to do it as well.
True, poor quality jpegs. Problems that you stated. Plus pattern mismatch on all sides. I didn't take pictures of these jpegs and I don't want too. Don't want to use jpegs. Therefore, I need to model my own textures and add color as needed. How do I model and create .P2M files without jpegs? How did SolidWorks create their textures. Their texture can be edited.
If you want to convert your jpegs to P2M in Solidworks here is the workflow I use.
1. Open any part or create a fake part
2. Apply an existing P2M appearance to this part (Solid>Red for example)
3. In your appearance properties go to the advanced tab.
4. Under the appearance file path, browse to your jpeg you would like to add (make sure all file types is selected in your browse screen)
5. Once you click on your jpeg and press open another screen will pop up asking you to save as P2M
6. Select your location and pick a name for your new P2M and you are done.
I created a custom appearance folder and put all of the P2M I created in this location. There may be a way to bulk convert to P2M but I am unaware of how if there is one. Hope this helps a bit. As Rob said though the tile effect will be because of file size and quality. I usually try for the largest size possible to be able to be scaled down or tiled as needed.
Rob, I will definitely be book marking that link. Thats awesome information.