Sorry, I have not tried the HE-4... but isn't that one quite difficult to drive? According to specs it's almost as bad as the HE-6, and my HAP-100 was not nearly sufficient for that.
I saw your other thread where you're looking for a new dac and maybe replace the preamp as well. The Benchmark Dac2 you were looking at may have enough. I haven't heard the Dac2, but a friend of mine has the Dac1 and it has a rather beefy headphone output.