I believe I might have to photograph the artwork in sections and then somehow stitch it together in GIMP or Photoshop or whatever software would do the job.

Don't waste your time doing that by hand in a generic image editor. Use a tool designed for the job, such as Hugin.

Hugin is most commonly used for semi-automatically stitching together large panoramic images from multiple shots taken from the same spot, but it can also handle stitching together a flat painting or mural from pictures taken from several different camera positions.

There's a very nice tutorial on the Hugin website titled Stitching murals using mosaic mode by Terry Duell which describes how to do that. Rather than try to replicate the tutorial here, I'll just briefly summarize the basic workflow and highlight the main ways in which the process differs from ordinary panorama stitching (for which there are also plenty of introductory tutorials):