JA, some bad news and then some fairly good news (but, Spoiler Alert, ultimately not that good), and then some more bad news again.
A PDF in InDesign is just another image, and, as for other images, you cannot 'read' text out of it. A PDF is not imported as a set of graphics, text frames, and bitmap images, but as a whole -- exactly as an Illustrator .AI file is imported in its entirety only so you cannot edit text "in" it. That not as much put limits on what you can do inside InDesign itself, but is in fact a show-stopper right here and now.
Back to Bad: due to all possible compress/subset optimizations in the plain text inside a PDF, there is no guarantee that any tool can actually read it -- up to and including Adobe Acrobat itself! If you work with PDFs on a regular basis, I'm sure you've encountered the odd one from which you simply cannot copy text out of it, and all you get is random garbage.
By far the easiest way to tackle this particular problem would be to entirely avoid post-processing PDFs. After all, they came from somewhere else -- it may well be easier to use the original data files for your purpose.
Thanks for the bad news (grin). At least it will save me a lot of time and perhaps a few ulcers as well.