Welcome! And sorry about your wallet. It will evaporate.
Warning: TL;DR, but I promise I have decent stuff to say.
You chose a great set of headphones. However, they are really hard to drive (I don't mean volume wise, I mean the ability to control the DT's) - but once you do, they have amazing potential...
Anyway, With all respect for Essence supporters, I think the DT880's are going to be severely hindered (compared to their immense potential) with pretty much any internal sound card or Xonar-ish (consumer-ish stuff). They are very tough to "drive", I mean, control.
I can, however, say that Jan Meier of Meier Audio designs his stuff especially tending toward the DT880 (and also the K701). He does have some stuff in your price range
And if you want fantastic bang for the buck, Audio-GD has stuff that is way underpriced because of the stigma of Chinese products (definitely not deserved in his case). He should have stuff in your price range (but note he hasn't really bothered to take his site out of the 1990's and the purchase procedure is a bit primitive.) I promise you, though, his stuff is an amazing deal.
Schiit audio has a nice following here, too, and they have a really good return/trial policy. Everyone who owns one of their amps seems to love them. I can't say much about them them as their sound signature when I tried one wasn't my personal cup of tea (everyone has their own preferences, and you, if you're like most other people, will love them).
Now for a dream: I'm assuming you don't want Vacuum Tubes. But if you want to do those glowy Soviet-era things some day (and want to double your current price bracket, which is probably inevitable in the near future, now that you've joined this site), Woo Audio's WA2 is adored on this site for it's synergy with the DT880.
