This might have been mentioned elsewhere, but pay close attention to the DETAIL/NOR/EDIT switch.
EDIT mode still uses the internal TBC, but bypasses all other digital processing; therefore, the Soft->Sharp slider has no effect.
You'll want to use EDIT mode if you plan on doing a hardcore/purist preservation. Averaging multiple captures will significantly reduce the noise anyway.
If you want to use the Soft->Sharp slider (DETAIL or NOR mode), then that's fine, as it works rather well and whatever artifacts it produces (due to frame averaging) are hard to notice.
JEDIT: You might also want to consider using a Panasonic DMR-ES10 DVD recorder if the recording has any wiggly lines.
QUESTION: You're using the s-video output of the Panasonic AG-1980, right?