I need to copy both image and text at the same time

I have a pdf with a bunch of images that have text inset, and I need to extract the images while keeping the text in its proper position. It would take too long to explain exactly what it is, but just think of it like a comic strip. The drawings and the word balloons are treated as an image, but the words inside the word balloons are treated as text; you can't select them both at the same time.

I know that I can do Snapshot to get both image and text, but it doesn't intelligently find the edge of the image like it does when you're just selecting the image by itself, and it doesn't paste in the image's native size (this part is less important, but the edge-finding is very important). Is there a way to preserve those functions (to save me from additional image-editing steps for each of the many images in the pdf) while still copying over the text as well? It would save me a ton of time if I could just do that all in a single step (there's over 300 images).