Here's a page ("Good PDF.pdf") exported as PDF from Dorico, music notation software. It uses the Qt framework for its PDF generation.
Designer imports it almost reliably (let's forget about ligatures for the moment).
However, if I re-save the PDF in Preview (or other PDFKit processes), the import goes completely crazy. ("Bad PDF.pdf")
Interestingly, an EPS of the Bad PDF (still with embedded fonts) imports perfectly, as outlines. Converting the EPS back to PDF yields the same crazy results.
Bad PDF.eps
Bad PDF.pdf
Good PDF.pdf