The 6.2s were designed to be tube friendly, so your tube idea sounds like a good one to me.
Each generation of DACs seems less "digital" than the last. The Neko DAC I've had home for a few weeks has no hint of the usual scare words associated with digital: harsh, grainy, bright, lean, threadbare, etc. The Neko has a 30-day money-back home trial (end of sales pitch; I'm just a happy customer.)