Recommendations for headphones under $400?

So now I have a new problem that makes me think I must be missing something but if there are any Hegel H300 owners here maybe they can chime in.
I am now using a Hegel H300 integrated for my system and this does not have a headphone socket.
No problem I thought I will just connect a headphone amp to the pre outs of this amp.
However Hegel appear to have designed this unit so that when you mute the music through the speakers it also mutes the output to the pre outs.
This sort of defeats the object of my usage unless anybody knows a way around this.
I have emailed Hegel themselves but as of yet still awaiting their reply.

Hi uberwaltz,

     I'd be very interested in Hegel's rationale for not including a high quality and convenient method of connecting headphones to their top of the line $5,000 integrated amp while the vast majority of their competitors do so, often at a fraction of the Hegel H300's price.  WTF?

     It's commonly known that extreme cold slows down cognitive functioning.  I apparently incorrectly assumed the execs at this Norwegian company would be making these critical decisions indoors with the heat on.
     Did you know it had no headphone accomodations when you bought it?  On an integrated amp, that would be a deal breaker for me and likely many others.  
     
     If you don't want to sell your H300 and buy a more headphone friendly integrated, the only solution I'm aware of is buying an external headphone amp/dac with a digital input, se or xlr analog outputs and a headphone jack.  
     The procedure for hooking up an external dac is detailed in your H300 owners manual.  It basically calls for connecting the H300's digital output to the external amp/dac in what Hegel calls a DAC-loop. I learned of this on the linked thread here:
  
https://forum.audiogon.com/discussions/adding-a-dac

Tim

My understanding was using Pre-Out completely removes amplification and speaker output from the unit.Don't use Mute,you still have variable output from Hagel to the headphone amp but that shouldn't be a problem,set a level and forget it...

@freediver 
That was EXACTLY my assumption too which is why I was not too worried that it had no headphone jack.
However it does not, anything connected to the pre out is subject to the volume pot level BUT the music is still conveyed via the speaker terminals.
It would need a speaker off option or the pre outs changing internally to line outs.

@noble100 
Unfortunately that is exactly what it says, a DAC loop only.
It would work if all I had was a digital input to the Hegel but it will not work with any of the 3 analog inputs I have.
There was a thread on the very subject back in 2016 with someone having exact same issue.

Maybe the Norwegian designers had not drunk enough beer before thinking this one through.

Yes it is becoming a deal breaker....
Yes I knew no headphone jack but as stated I wrongly assumed the pre outs would do the job