All, I haven't read the entire thread, but I too had a muddy tone that was boomy with HB's but ok with sinlgle coils, from a stock sIII I built in December.
I started by changing the power section cathode bypass cap from 220 to 50uF/50v. That tightened it up a bit. Then after reading some posts on this forum, I check that plate dissipation and current through my JJ tubes using a 120 ohm resistor (actually measured 123) and it was at about 43ma per tube and 14 watts PD; way too high. I located two power resitors (totaling 150 ohms) and installed them to test. I'm amazed at the clarity and how articulate the amp became. Therefore, I changed backed to the original 220uF cathode bypass cap and all is good. The tone is magnificant, and now the tubes are running at about 39ma with 13W PD.
So, use that for what's it worth and see if you get the same results.
Also, coco being the gentleman that he is, has mailed me a 150ohm/5W, keeping his word.
I'm couldn't be more pleased with this amp. It rocks.
Just FYI - I'm playing through a 2x12 W* bomb - a 30w alnico blue dog and a 50w ceramic silver bell.