Best 6DJ8/6AS7 combo

I am currently using a David Yee output transformerless single ended dual triode headphone amp, with an early 70's TOTL Bugle Boy 6DJ8, and an RCA grey-plate 6080. I also have an RCA black-plate 6AS7GA that I found fatiguing in the early stages of using this amp.

The sound of this setup is clean, neutral and balanced. But I am looking for a bigger, more powerful (but controlled) bass, full, natural and lifelike timber and harmonics (like a good DH SET), great soundstage and imaging, and (especially) zero fatigue!

My headphones are the somewhat bass-light, but otherwise completely neutral and transparent JVC HA-D990.

My sources are a Micro Seiki BL51, with a Grace 707 II tonearm, and a Signet TK7e cartridge feeding the world-class phonostage of my Accuphase E-202. A Philips Little Giant DAC + triple filtered LPS being fed by my Carver MV-5 which is serving as a transport.

All of my cables are neutral and transparent hi-end designs (pure copper).
 
Well, maybe try some 6922's or E88CC's or even some 6N1Ps in place of the 6DJ8 if your filament supply can handle twice the current. Compared to the rest of your system, it's a cheap experiment.

I'm using some NOS JAN Philips 6922's and JJ E88CCs, obtained from Tube Depot, in a Noval socketed preamp.