@nickbatz Thanks for your response. Good to know re: AF print dialog drivers, though I am using Windows and not OSX.
I do have the ICC profiles for my papers. I am actually using Canon Pro Lustre paper for this print. My workflow doesn't normally involve printing from PNGs, it was just something I tried that happened to work.
I think the problem here is that for 32-bit depth images from e.g. HDR merges, no (reasonable) print driver would accept such a format, but Affinity Photo does not issue a warning or convert to 16-bit before sending to the printer. I would consider this not particularly user-friendly. Maybe this is a feature that could be implemented, or at least a warning could be raised with an "Are you sure?"-style dialog.