Recommendations for headphones under $400?

" I still could have my h300 internally modified to convert the existing pre out to a full line out independant of music through the speakers."

Hi uberwaltz,
     I didn't know this was even an option and you were considering it.  If it's not cost prohibitive and there's no real downside, this also seems like a good solution to me.  But you seem to prefer an 'all-in-one' solution more than having a separate headphone dac/amp.  
     I understand your reluctance to add a dac and amp or a dac/amp combo to your system because I recently had to make a similar decision with my system.  I decided to add a separate dac and class A headphone amp to my system located right next to my listening position. 
   
      It's just a small JDS Labs dac into a small Aune x7s small pure class A amp putting out a maximum of 2 watts but I'm really enjoying everything I listen to through them with a pair of Sony Z-7 headphones. Class A sounds extremely good in my opinion. If you're interested, you could do something similar with just a good class A headphone amp (no dac required) and the very good Hifiman 400i headphones, once a mod is performed to your H300 pre outs. 
      I think the 400i's would sound exceptionally good utilizing the H300's internal dac outputted through true pre outs to a good powerful external pure class A headphone amp.
     Hopefully,  auditioning an H160 in your system will help you decide which option you prefer.

Best wishes,
    Tim   

To anyone using Grado SR type or the similar looking Sennheisers or really any headphones that employ foam ear pads, like say, Sennheiser 600s, what I found out recently was that foam pads are very messed. The sound is much much better simply taking all of the foam off. Not only is the foam material BAD for the sound but it makes the ear too far away from the transducer so you lose dynamics and volume. One wonders can these people even hear? What were they thinking?! I’d opine the sound is at least twice as good. Super good! You can see what I’m talking about right away if the foam pads on your headphones are removable. Then the trick is to find some way to make the surface of the headphones soft so they won’t kill your ears, I’m using gel strips right now that work fine and keep the distance from the ear to the transducer small. If someone has a better solution I’m all ears. Unbelievable! I’m not hot dogging you. 🌭

Who would have thought that such a simple quest would turn into such a gnarly affair!

Tim, yes it is a possibility for a qualified electronics engineer to perform, have not researched price yet but still an option.
The h160 may end up being the most sensible option as modifying the h300 might seriously deter potential future owners.
Still also seems a darn shame to have that doorstop of a BAT amp sitting idle too.
Maybe I just buy more speakers and make 3 or 4 systems!

@geoffkait
I truly believe you and agree totally, but it is the hassle of finding something comfortable to replace those foam pads.
I had an old pair of Sennheisers that had sat in a cupboard for 15 years or so and the foam pads disintegrated but I tried them anyway and was pretty impressed with the sq, not so much with the comfort level!
This was a few years ago and as they were only a $40 pair of cans they got tossed. And the experience forgotten about until you mentioned it to jar these foggy old grey cells

" The h160 may end up being the most sensible option as modifying the h300 might seriously deter potential future owners.
Still also seems a darn shame to have that doorstop of a BAT amp sitting idle too.
Maybe I just buy more speakers and make 3 or 4 systems!"

Hi uberwaltz,

I would think that modifying your H300’s pre outs so they function as true pre outs would only increase its value since others would likely realize the value of this mod just as you have.
Your Bat-VK600SE is an expensive, well respected solid state amp that you’d likely be able to sell for a significant price if it’s in good condition. Why not sell it to finance the H300 mod and a good headphone amp? You’d also be freeing a good amp from a doomed fate of collecting dust in a closet to do what it was made to do: drive high quality speakers with high quality amplification.
I would suggest the following course of action:
1. If you like the performance of the H160 in your system once you audition it, buy one and sell your Hegel H300 and Bat-VK600SE.
2. If you like the performance of the H300 more than the H160 in your system, have the mod done to your H300’s pre outs, buy a good external headphone amp of your choice and sell your Bat-VK600SE.
3. Avoid buying more speakers and making 3 or 4 additional systems.

Scenario #3 only proliferates the number of your home systems in which you are unable to have a good and convenient method of listening to headphones in.

Both scenario #1 and #2 ensures you have both a good amp that you like driving your speakers and a good amp. either internal with the H160 or external with the H300, that you like driving your somewhat inefficient Hifiman 400i headphones.

I hope my suggestions helped you a bit,
Tim