I plugged my iPhone SE into an amplifier and turned the iPhone's volume to maximum to get the best sound-to-noise ratio.
The health app says that my noise exposure was "Loud".
Did the health app measure the actual sound level or was it basing its warning only on the volume level?
The health measurement assumes you are using wired headphones in your ear and not that they measure the sound. Do you have an Apple Watch to try and gauge the sound pressure of your speakers or another independent device?
How you get the audio out might matter if you can get it out digitally instead of using the analog amplifier to crank the signal to the max. Using an USB based external DAC is typically the best path to high signal to noise audio from any iPod, iPad or iPhone.
Classifying the speakers over Bluetooth has worked in the past, but we would need to know how you are passing the signal to dig into this more.
