Does your TV, projector, apple box have a digital out? or even lightning cable out, you can get a USB from the lightning cable and use that to feed an outboard DAC. get a decent DAC and skip the HDMI all together. Schiit audio for example has DAC's in all price ranges.
there are also HDMI to USB audio converters out there. they are dead cheep think $20. google it you will need one that works with IOS I'd imagine.
there are also HDMI to USB audio converters out there. they are dead cheep think $20. google it you will need one that works with IOS I'd imagine.