Audio Greetings all, what would be a good headset for me, in an affordable price range?

Xogroroth

Recruit
Hail;

I am a 52 year man, severe Aperger's and severe ADHD, both which I consider a blessing.

I am also tone deaf:
High and low frequencies are picked up very well, midrange tones ... a loss up to 70%.
While the average human can hear inbetween 20Hz and 20KHz, I hear tones as low as 6Hz, and as high as 20900Hz.

Headphones usually cut of at the 20Hz - 20KHz (or so they CLAIM, many cut of much sooner in reality, often even at 40Hz, of those I had. One good exception was my Shure which had costed 80 Euros, and lived an incredible 8 years. This one went even from 10Hz to 22KHz on my friend's sound test bench, years ago. He sadly past away.).
This kind of headset (especially for the price!!!) was an absolute phenomena, never heard sound like that before.
The deepest bass (that is, NORMAL bass, not the "bass boosted" stuff, obviously) came through crispy clear, no deformation, at all.
Just "wunderbar", to go with Tenpole Tudor.

Alas, I never had anything like this before, nor after.
One that came darn near, was my father's old headphone, one with a 6.35mm jack, stereo.
It had serious wear, but used it for 3 more years ... until my dog figured it looked like a nice meal. :S
Probably not so much a music nut as myself, I guess.

Each time I enter a store, I get to hear how "phenomenal" this one is, or that one even far more "phenomenalastic", you know, buyers talk.
According to them, they sell headphones that go from -1KHz up to 5Mhz, if you let them talk enough.
I never do, I ask them to let me test it, but then they usually tell me, that particular one has no test set, or I get to test it on a crappy setup, on which folks have been messing with a lot of settings.
In the rare cases I get to get a good setup to test it on, the promises fall dead the moment I hear the sound. :(

And thus ... I came here, having asked on Quora, Reddit, and several other sites, but never getting any decent answer.
For one, many just do not seem to believe me, even if I showed them the results of my hearing tests.
I hope, I will get a serious response here ... .

Thank you, aforehand.

Kindest regards:
Xog.
 
The Beyerdynamic DT770 Pro has a frequency response of 5Hz-35KHz.

Some reviews mentioned that the sound reached as low as 10Hz in their testing so I'm assuming the published range is legit. I had a pair of these sometime ago but I cannot confirm it myself as my hearing barely covers the normal range haha!

It has a V-shaped sound signature. Since the mids are already a bit recessed and treble is spicy on these Beyers, you probably will need to use EQ to get it to your liking.

There is also a new DT700 Pro X which has an even wider range of 5Hz-40KHz. I have not used it before though.