Just to close this one out, I guess I was lucky and my proposed setup worked. It turns out the Lepai LP-2020A+ has two line-level inputs: RCA and 3.5mm. It appears that these inputs are internally connected via a simple Y (instead of switched) and feed a single input on the amp. Since it was basically a splitter, I ran my source to the RCA jacks and used the 3.5mm as an output to the sub. I think the quality limit is the amp, not this hacked-together setup, so it's getting the job done until I get a new receiver.
As an aside (and since I know this is the sub forum, not amp), the Lepai amp is a pretty amazing value at $22. The sound quality is decent, although I do hear an low freq hum from time to time (but not always) when the amp is on but no music is playing. I am feeding it with a 50 ft RCA cable, so it's possible that the cable is acting as an antenna. It's also possible (as I've read) that the crappy brick transformer is sending dirty DC. In any event, when music is playing, it sounds great. My only real gripe is that the volume knob has a very bright blue LED which can't be disabled. I may crack open the case and kill it. Also, since I'm using a powered sub, I can't say how it would do with regular bookshelf speakers.