LOL, Melissa! Yeah. It pays to check sizes. I've ordered an occasional stamp without checking dimensions & it's usually smallerr than I wanted. That said, howerver, your experience is a new one on me. I've purchased various images that are produced in more than one size because I liked the image & could see myself using it in both sizes. Some of these multiple size stamps were available as just rubber, cling & woodmount. In every case it didn't matter what version I got, the die was always the same size for all 3 options.
If I understand you, the dies are different sizes in your case? Since we all know that stamps are cast in molds there must be 2 separate molds for this image. Here's what may have happened with JoAnn's... They had a stock of the larger in cling back & a stock of the smaller image in woodmount.
Far as using just parts of the larger image. Yeah. I've done that with some of my larger (4x6) stamps--not all of which are BGs.
Thanks for the 'PSA/FYI', pal! Would love to see the image.