Just as I imagined, I defiantly know what the problem is now. If I had to use the WA6 stock I would sell it. The stock Shu Guang is thin and a bit harsh. The 6DE7 are just okay. Also factoring in pre-break-in on the cans, yes your experience is exactly what I went through. Not to worry, with a little bit of cash and some patience you will have a completely different setup from what you are hearing if you decide to take a leap and keep your setup, with some slight modifications of course.
First off, the stock rectifier is garbage. Opt for a UE596, Sophia Electric 274b, Mullard GZ34 or even a vintage NOS 274b like the Sylvania or RCA (1940-1950ish). For around $60 it would be a good upgrade. Obviously the first three mentioned are better but if your on a budget the last should suffice. Also, opt for new driver tubes, I went with 6SN7 because they sounded full and offered very punchy bass which I like. Again, NOS sylvania are a great bang for your buck at around maybe $60-$80 with adapters. Some people like 6GL7, there are a number of driver tubes to choose from.
Give the new tubes time to break in, as well as the HD650. I have slight adjustments on the EQ which dialed everything in, this will help you achieve that sweet spot. Also, make sure your source is top notch and everything is configured correctly (clipping, bit rate etc).
It's going to take some work but it will take your listening to a whole new level. I consider myself a bit of a basshead and I would never part with my HD650 or my beloved Woo.
Good luck!