Best phone/personal listening device under $500

^^^YES,the Camera Adapter bipasses the Apple DAC & sends a direct stream,doesn't matter whats downstream as long as it has Digital Audio in & built in DAC....This was really big years ago...

Does this mean that I am bypassing the internal DAC in the phone and solely using the USB DAC for the digital conversion?

Yes, at least it does using the Apple Camera Adapter with the Dragonfly.  Can’t speak to the Microstreamer. 

Definitely look at the lightning to USB->Dragonfly red or Cobalt it's a setup that doesn't add a ton of bulk.  The Onkyo HF player allows you to play FLAC files which is what made me go in that direction with an iPhone awhile back.  Not mind blowing but very good sound on the go.
Yes the Fiio players are good for the price I picked up a little M3 I think it's called recently which is an apple watch sized touch player and it's surprisingly good for the money and its size.  Maybe even better than the Dragonfly Red.
It's too bad the Pono never took off or evolved it was a really fine sounding DAP with mediocre form factor and battery life unfortunately...

All good advice. I sold my Chord Mojo for the same reason. It didn’t have the dynamics and soundstage I wanted. I’d go with the Fiio product line. Great value. 

Thanks Soix
Does this mean that I am bypassing the internal DAC in the phone and solely using the USB DAC for the digital conversion? I have a HRT Micorstreamer that I can connect but I thought that there may be an issue with how the data is sent to the external DAC via a iPhone - meaning that the D to A conversion is done with the phone DAC.
GLR

I use my iPhone with the Apple Camera Adapter and an Audioquest Dragonfly Red Amp/DAC into my HIFIMAN HE400S. Sounds MUCH better than direct out of the iPhone, and it’s extremely portable and perfectly comfortable to walk around with to the point you barely know it’s even there. And at $200 for the Dragonfly Red (or around $150 used) and 30 bucks for the Camera Adapter you’re at less than half your $500 limit. Best of luck.

Well my recommendation then would be the M6 DAP from FiiO.

Hi

I love my current headphones and so I am trying to work with them as my “baseline” equipment and find the source that will work well with them.

I’ve read that a LG V30 phone might not be a bad low cost option...

^^^I’m sorry Mr.dealer but in my direct comparrison with iFi the Chord is overpriced & didn’t image as well...
OP:Instead of adding or changing gear why not get a good set of Bluetooth headphones?

The Chord Mojo is the best portable DAC in this price range IMO.  Wonderful unit and punches way above it's price range.  You do need the Apple Camera adapter with it which I think is like $30.  I am a little biased as I am a Chord dealer but if you read the reviews, everyone loves that unit.