With that kind of budget, I suggest you audition the Senn HD800, LCD3/2, Fostex TH900/600, Beyer T1, ATH 3000Anv, etc
Choose the one that give you the most satisfaction..

We also don't know what type of music you listen and what will be your source
Normally, we choose the headphone first.
From there, we try to find the amp, DAC, source that bring out the best synergy or can make the headphone sings....
No matter what amp, DAC, source, accessory, etc you change, you won't be able to make an HD800 to sound like an LCD3