Am I doing it right? Upsizing images for Print-on-Demand

I am trying to increase the size of images to use for various print-on-demand commerce sites. My original images are produced at 960 × 1568 pixels, with an image DPI of 72 pixels/inch. Processing in Adobe Lightroom, I use the Enhance feature on each image. I then export them at 20,000 pixels (on the long side). When I upload to the Print-on-Demand sites (i.e. SOciety6, Zazzle, etc.) they seem fine, and are accepted for the required dimensions on most products. However, I worry that I am not clearly seeing the resolution on the individual products.

My question is this: is this the right way to get the highest resolution for my images? Am I losing quality in some way? I use Lightroom a lot, as it can do bulk processing of hundreds of images at a time. I also have Photoshop, but haven't used it much. Can anyone offer any insight into the right way to perform this process? I appreciate any input!