I've had no problems with printing included pdfs and tiffs in AC10, and I've used both methods (figure tool and external content) you describe as well as direct printing from the model floor plan.
- download the last hotfix (1188) for AC10 if you haven't got it (Help>Check for updates).
- check that you're
printing, not plotting.
- check that you've saved a layer combo that includes the pdf layer, and that it's set for the view in question on the layout.
AC4.1-AC26SWE; MacOS13.5.1; MP5,1+MBP16,1