Artificial distance?
That really does not make any sense at all. In order for some distance X to be artificial, some other distance Y must be natural else there is no way to differentiate the two.
If I listen to a performance of a symphony while sitting in the orchestra pit, is that natural distance? What about the front row? 10th row? 50th row? 1st balcony? Second? Third? Left side? Center? Right side?
What is "natural distance"? If we cannot answer this, we have no reference point to declare something artificial !
The only possible conclusion is "there is no natural distance", only distances you prefer for personal and subjective reasons.
Davesrose for example explicitly prefers the perceived "distance" of Sennheisers in general. This doesn't mean you will or wont however. If you want to give Senns a try, I would recommend getting the 555($95) or 580($125). (amazon prices)
In one of your previous posts Davesrose, you suggested that "AKG's need a warm source where Sennheisers need an accurate source".
The opposite of "accurate" would be "inaccurate", and when you translate "inaccurate" to the audio domain, "innaccurate" = "distortion".
Distortion changes our perception of the sound.
When people say they want a "warm" source, what they are really saying is they want a source that changes how the signal sounds.
You are quite vocal in your sennheiser preference, so when auditioning an AKG for example, you are consciously or subconsciously comparing it to the sound you prefer, and realizing that it is different (which it's meant to be), decide "it's missing something". And so, perhaps a "more distorted" source may change it in a way you prefer.
My amp of choice for my K501's (Headamp GilmoreLite) is about the polar-opposite of "warm & distorted". It is what an amplifier should be---a device to add gain to a signal---nothing more. I much prefer this over other tube offerings I auditioned. The whole point here is if you dislike the sound of a headphone, and you are hoping that adding distortion to your source will make it sound better---your priorities are reversed. Keep your source accurate and find a phone you like.
This forum would be alot more helpful if people posted a bit more information in both their questions and answers, as opposed to simply saying "I like X because it's present where Y sounds recessed". Short sound clips(even 10 seconds), and descriptions of your experience with them on your setup would go a long way to accomplishing this.