There is current in the battery. This is causing inter-stage modulation.
A little more filtering and the battery current is steady. If you want a high Z output this is a good time to address that.
When adding the filter on J3's drain you can use it to feed a high Z headset. I'm showing a dual output. In this sim we have a headphone on the source and drain of J3. So you can connect it to your favorite crystal set and share the listening experience with a friend.
If you don't have the 2SK2539 you can build the circuit with any Jfet. The biasing may require some adjustment. I substituted J112s and it still function but at a lower gain.
Look at the first set of curves on the last post. You would need a 3.3K Ohm or 4.7K Ohm resistor with that Jfet to get 1 ma. It would function if built using the 1K Ohm but would have a very high current drain on the battery.
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