The F1J only puts about 1 Watt max in 50 Ohms, voltage limited. I got this from the maestro himself. According to Ohms law the impedance will determine how much current will be drawn, and 50 Ohm is not a nasty load that calls for a speaker amp.
So this - again - tells me that wattage / ampere is not the primary concern with HE-6.
However, the F1J is supposedly a very clear and transparent amp, but as I said, according to Nelson Pass it's not delivering more than about 1W and thus not more than many high powered headphone amps - actually much less. My Soloist, which has been doubted by some regarding the HE-6 is at about 1.7W, then yields considerably more than the F1J, not to mention my Audio-gd Master 6 which is 7W in 50 Ohms.
What this is more likely about is that the HE-6 has slightly too much treble (and with velour pads also less low end than with stock pleather). Especially the velour pads may give you the impression that it needs more power / current, but in fact it's the frequency response with these pads which is the issue. With pleather pads it's better, but there is still a little too much treble. This can't be fixed with extra power / current IMO. However, it can be fixed with other pads or felt or whatever it takes to absorb some of the excess treble. And subjectively, if you turn up the volume, you experience more low end also which will sound more balanced and you experience more details too.
Paying to much attention to the Watts again. Also Potterma has a different calculation.
Anyways, again, in my experience it's more about the current reserve a amp can maintain. Speaker amps with the size of their transformers are able to keep more current in reserve when compared to headphone amps. Yes, some headphone amps can put out mega watts - so what? They don't have the (current) sustainability that speaker amps have when really complicated music passages calls for it - headphone amps tend to run out of gas - so to speak . The headphone amps transformers are way to small, some of them even use r-core / c-core transformers. The transformers in speaker amps are the size of the entire headphone amp at times. Headphone amps are meant to be designed for a small foot print (most of them) this limits them with the size transformers they are able to use. Speaker amps don't have this issue.
I don't know if this has been discussed before, but I think one of HE-6's greatest faults is its screw-in connectors. This has got to be the worst type of connector I've seen in any $1K+ headphones with detachable cables. The problem is that need I screw the rotatable portion of the connector into the headphone, but since it's so small it's difficult for me to screw it with my fingers all the way. It's difficult for me to apply enough force into it, so it's nearly impossible to screw it all the way (thus ensuring a secure, tight connection) with my bare fingers only. The connector still feels somewhat wobbly, and turns around a little too.
Is there a solution to this problem? Perhaps a tool that I can use to screw it all the way (without damaging the headphone or the connectors, hopefully), or a smart method to get it done without a specific tool?
Yes - Get them Hardwired.