Huh, are he-300 really that bad? It needs to be and open headphone so 558 comes to mind, but they have to be casual listener friendly with a little "oomph fun", so he-300 seemed like a good option.
Philips X1/2? Works from a DAP and might not have the midrange richness of a HD558/598 but still pretty decent. Try them first though.For a steal you can get a HD595 in good condition, equalise it when used in a PC/tablet/phone/DAP-set up and done. The mid-fi market is so saturated you can get great gear for little money.
I read on reddit about the hifiman he6. Does it do anything special that other headphones can't? I have an lcd2 with fazors and a lyr 2.
http://www.meier-audio.homepage.t-online.de/amplifiers.htm(If you're annoyed by sibilance, how can you stand SRH940?)