I threw this circuit together last night to get an idea of what such a circuit might sound like. I'm using a 6247 sub-miniature triode as the input stage, which drives an LM386 power amp.
I didn't do much math-ing to figure out the bias point with a tube at such a low voltage. The cathode resistor just needs to be low to avoid horrible distortion, hence the 82 ohm resistor. I think the tube actually drops signal level at such a low voltage, since bypassing the tube in the signal chain actually resulted in a boost of volume from the LM386. Keeping it in-line adds a little bit of compression but it's hard to hear much "tube-ness" beyond that.
The power amp in this circuit is a bit dissapointing. The LM386 is rather noisy, even with the massive filter cap there's still a high pitch whine that can be heard with my 32 ohm headphones. The moderately sized 100uf output cap provides plenty of bass, but it sounds rather mushy. I'd like to find a circuit that doesn't require an electrolytic cap on the output.
This circuit is definitely not an improvement on the input source. It's a good place to work from though, I think. The tube isn't noisy here, it's definitely the power amp that needs improvement. I'm wondering if I'll be able to make a suitable single-ended output stage with a small transformer and another 6247, or maybe just use a simple transistor based output circuit rather than a chip-amp.