It recently occurred to me that DSP radios like the Tecsun PL-380 and the C. Crane Skywave likely have a fixed-level audio output line on one or more of the pins of their SiLabs' chips.
Sure enough-- the datasheets for the Si4736/37/38/39 and Si4730/31/34/35 chips all share the same pin assignments for LOUT (left channel audio) and ROUT (right channel audio).
For the "SSOP" chip package (which my Skywave radio has) a satisfactory fixed audio signal can be tapped at pin #24 (left) or pin #23 (right), and ground pins #13 or #14. The "QFN" chip package in all SiLabs versions has the left/right audio on pins #14 and #13, with #12 being the ground pin.
Note that you can also just use another convenient ground (-) spot on the PCB for the ground lead.
The IC's pins are very tiny and close together, but If you have the proper soldering equipment and a steady hand, it's a simple matter to tap one of the audio output pins and ground. I used wire wrap wire for the connections and routed the signal to a small mono jack on the side of the Skywave. A convenient spot for drilling the small hole is near the opening for the wrist strap on the left side of the radio.
With an audio patch cord between the Skywave and my Tascam DR-1 digital audio recorder I'm not able to clearly record DX signals, without having to Y-split the volume-controlled audio from the headphones jack. Very convenient! The audio level is high enough to make good recordings without distortion. I don't know if it's a true "line level" signal, but it works great for my recorder.