Upgrade your DAC first, definitely (and maybe the digital cable as well). Improvements to the source often provide the biggest gains in my experience. I have the Elekit and HD650 and it's a good match. I alternate between a Virtue Audio Piano CD Player and a MHDT Paradisea DAC (with Western Electric D getter 396A). They're both excellent, the Piano CDP being the transport when using the Paradisea. I prefer both of these to a Cambridge 540C V2 that I also own.
You can also replace the stock tubes. Just about anything is an improvement over the stock tubes. GE 5 stars are good (these are older than the stock and older = better). For more money ($100-150 per pair), go for Western Electric 396A, especially the D getters. RCA's and Sylvanias are also better than the stock. I've tried all of these, BTW, and stayed with the 396A. Another minor upgrade is to get tube dampers from Herbie's Audio Lab. Don't bother with any other tube dampers, get Herbies. And get the better, more expensive type of the two he sells (they cost like $25 each or something). The tube dampers tighten everything up, esp. the bass, and smooth the highs a bit. One other minor upgrade is to replace the stock HD650 cable with a Cardas cable. Your best price on this is through DIYcable.com.