After some ripping and listening, I decided that the Linestreamer wasn't making the best of the signal coming from my Seduction- the bass was pretty thin. In hindsight, this should not have been a surprise, as the linestreamer has a 5K input impedance.
So I thought about getting some sort of buffer to match things up. But then it occurred to me that I already have resistors on hand, why not change the input impedance?
This is the kind of dumb thinking that often gets me into trouble. I had to remove the existing surface mount resistors and solder in the replacements across the tabs of the circuit board mounted RCA jacks. I had never played with surface mount stuff before, so visions of ruining an expensive board were dancing in my head. I managed to get it done without destroying anything, but it was a little scary.
The result is quite pleasing. With 51K input resistors in the linestreamer, the bass is much better, and the recording level is higher, but doesn't go into clipping. I think I was lucky, this could have gone wrong so many ways.
So I suppose the moral of the story is that the Linestreamer is not a good out-of-the-box match for the Seduction, but it can sound good if you can do something to get the impedance into a range the Seduction can deal with.