Preserving Text Copyability/Searchability in Imported PDFs

My group's work (using TCS2019) frequently involves incorporating PDFs from other sources (e.g., engineering documents and outputs from our pricing system) by importing them into frames in our FrameMaker books. Generally this works well, retaining the copyability and searchability of the embedded documents in our final PDF output... but recently I've discovered that documents from one source are not searchable or copyable in our final output, even though the PDFs I'm incorporating are searchable and copyable in their own right.

My preliminary read is that it's some artifact of how the providing group is generating their PDFs... but before I go asking them to change their process, I was wondering if anyone could think of something I might be able to do on my end to correct this? Something in the settings or properties of the input files that might be relevant, for instance.

FWIW, we use "Print Selected Files..." rather than Publish to make our PDFs, because there are some utility files in our book templates that we don't want to include in our output (and because in my experiments, Publish tends to hash some aspects of our documents). This may not be the optimum approach, I acknowledge, but in this instance I'm looking to fix a specific problem, not retool a longstanding (if potentially somewhat out-of-date) process.