Sorry for the late reply - I'm not on head-fi much these days.
I've had all over these except the HE-6SEV2 (and I probably won't end up purchasing one).
The 6 screw and 4 screw are much more alike than the HE-6SE was. Every time Hifiman has "rereleased" one of their classic headphones it's always sounded different. The HE-6se is probably the closest to the HE-6 when comparing the other "rereleased" Hifiman headphones. It captures a lot of the similar sparkle, but I suspect they did some of their diaphragm thinning.
Major differences between the original HE-6 and HE-6se:
-HE-6se is notably easier to drive.
-HE-6se has more bass and it tends to linger more (mostly midbass, not subbass)
-HE-6se has more treble overall and it starts peaking earlier
-HE-6 has better bass control
-HE-6 is more detailed
-HE-6 has a blacker background which gives it more attack/decay detail
-HE-6 is faster
-HE-6 has more midrange and less of a "U" shape emphasis
With the HE-6se I think a starting point to alleviate the treble emphasis is grill mod and changing out those stock pali pads.
Nice update! Did you try using the same pads? The old Velour pads and the new Pali pads probably contribute to some big changes.