Eyelids is one word.
"either I stayed like this and watched Andy sleep peacefully, with his head on my thighs, or I tried to get up without wakening him"
1. either I "stay" or "could stay" / or I "try" or "could try"
2. without "waking" him, or if you want to be like a fairy tale, without "awakening" him
3. Third option: dump his head onto the floor and go through his stuff.
Hmm... Andy's "a girl who can play an instrument like you can is very sexy to me" sounds rehearsed. It makes him sound insincere. Either Andy's about to pull a "score and scram" or you could stand to make his word choices a little less formal.
"Lay yourself down on the couch."
Why such precise instructions? Again, it sounds like this dude knows exactly what he's doing, like he's done it many times before (and run into problems that necessitated precise instructions). You have a number of options.
1. Andy really is just trying to "get some tail and hit the trail." In this case, you're doing fine.
2. Have Andy just nudge her toward the couch with no verbal cues.
3. Have Andy look over his shoulder toward the bedroom (perhaps worried about Sheena seeing the messy room/obsessive neatness/his My Little Pony collection and deciding that she doesn't want sleep with a guy who's messy/too neat/collects My Little Ponies) and Sheena pulls _him_ toward the couch.
4. Have Andy make a joke, like "If you're going to spend the night, is the couch okay?" and then either have Sheena joke back or just get to the yummy non-poseur lovin'. (This option doesn't work if Andy's not supposed to be good with words.)
5. Leave it as it is. Not everyone's going to fuss about this detail.
And on the mythology chapter! I do hope someone successfully completes a classical hero cycle, at least in a metaphorical sense.