I've had issues with diagnostics on machines that aren't set up perfectly - and that's without PAR. For example, installing ActiveState Perl for Windows to a network share, and then everyone copying the shared version locally (for performance reasons). (Not my design.)

What happens is that the diagnostics module will look in Config for where Perl is installed, and then look for perldiag.pod there. And that's where your trouble is. If only perldiag.pod were in the __END__ section of diagnostics.pm, PAR probably would incorporate it properly.

I know this isn't a solution - short of "don't use that module in a PAR-enabled app", I don't have one. Mostly because I don't use PAR. But perhaps that will help you track down a solution.