I have the Recon and the Omni and I like them both. The Omni does sound better, though, if you don't need console compatibility. Sounds like he doesn't (quoted below). I'd easily recommend the Omni -- grab one off AWD and save a few bucks and get SBX instead of DH. :-D
I don't know if the HP200 is "better" than the X1, just that I prefer the sound signature of the HP100 (different can!) to the X1. Regarding the ear cups, I honestly found the fuzzy, memory foam pads on the X1 to be kind of warm. I've never had a heat issue with my HP100, even though they're closed AND pleather.
@Change is Good can maybe speak more to the heat on the HP200 from first-hand experience, or you could ask in the HP200 thread (since he's the only person in this thread who has one).
Regarding your sound card choice, if you don't NEED the portability of the E3, the Omni does everything else and it's already out. You wouldn't need the E17 with the Omni. You wouldn't actually need another amp for the X1 or the HP200 (though, like I said, the X1 will sound slightly better with a little more amping).