A couple of points.
IPhone apps can be quite accurate, as they all are calibrated to the same standard. Android phones, unfortunately, are not. On my Samsung I had to use a 15dB! Sensitivity adjustment to match a calibrated sound level meter.
+1 for having a sound level meter.
On OSHA standards, be aware they are based on minimizing hearing loss related to speech intelligibility, and so do not consider loss above 8kHz. So high frequency loss is still possible while staying within their exposure limits.
I typically listen with 75-80 dB peaks measured with fast dBC settings.