what dacs are fast, lively, energetic?

Chord, but too much of a good thing for me. Too fast, sibilant, too bright, too detailed......like a racoon on crack. Not that it is not well designed or made, and I could however see it being valuable in a "dark" or a system that is lacking detail

I submit you must think about "system context". Components, including DACs can sound different based on the system their in and the end user's ear. 

@squared80 I’m curious - why do you find that hilarious and sad?

When I think about a lively/fast/energetic DAC, my brain first thinks of Chord. I don't necessarily love them in my system but I respect what they do. The TT2 can be had within your budget and it is popular for a reason.

Also look into Rockna. Their Wavelight DAC is very fast and clean, I like it better than the TT2 in my system. The big brother Wavedream might be an option if you can find a 2nd hand example. The balanced model and the signature edition are much higher priced but I think the regular or original version goes for under $5k sometimes.