Following up on that. I added a 6V source just for the heater and terminated the LM317 current source into ground. Low and behold I see a +/150mV sine wave at the output. I don't know if a real 12AU7 would be happy with a plate voltage of 12V (the DC operating point) but the model works with it.
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David Schultz
"The cheeper the crook, the gaudier the patter." - Sam Spade