Gave them a good listen tonight, I've only been using my lcd2f with the lyr up until tonight, so it was good to give these a go.
I have a Schiit loki as well, and as always when I first begin a listening session with the he5se, I'm at first tempted to tweak it ever so slightly, but I resisted and it only takes a few songs before my brain gets used to the hifimans signature. I queued up a lot of female singers because you said that they were primary concern.
I've always felt that the he5se, for all of its flaws, had some of the best imaging and soundstage of any of the planar headphones that I have heard, and I am pleased to say that the lyr 3 did well at accenting the stage, giving it a nice holographic edge. For that alone I would recommend the pairing, but in addition they did help to reduce some of the flaws that are innate to these headphones. And most importantly, I felt vocals were staged right in center and close where they were supposed to be, no thin sounding vocals here, very rich and detailed. Speed and prat were excellent. I would have to listen more (and indeed I will) to give any more details here.
As for negatives, could use a pinch more bass, and at the end of my listening session I did test a minor tweak on the eq of the loki, and it gives all the bass you would ever need, these headphones do respond well to the analog eq of the loki. The dip in the upper bass/lower mids are still there, but that is more the headphone and less the amp, I feel it is less present on this amp then they were with my fiio x7 ii which was my previous favorite pairing with this headphone. Also, a tiny adjustment on the loki is all that is needed to remove if you feel so inclined.
All I can say for now, will say that this amp is my new favorite pairing, I did not feel that these headphones paired well with either the magni 3+, nor the jds elemental. Both of those pairings accented the negatives of these headphones and my loki eq did very little to mitigate it. YMMV