It may be a foolish question, but WHAT did you not like about the sonic signature/sound of the HE-6 (on the various amps you tried) and what would you like to 'change' to the HE6 sound... what the amp should be adding/changing in the sound I mean?
If you want to go louder than going from Ember (around 2W) to Lyr (around 4W) is just 3dB. The 5W Mjolnir will add another 1dB.
a 250W/4 Ohm amp will be able to bring 20W to the table...
The HE-6 may not like that as it is rated at 6W but can easily handle short peaks of 20W I reckon.
It will play 6dB louder (substantial) than the Mjolnir.
With 20W the SPL would reach 120dB !
If it is a sound signature/quality issue than finding an amp that changes the signature THAT much will be hard to find IMO.