I think I should definitely increase the exposure time, though I'm not sure exactly how much. The 15 sec exposures came out very very dark on the computer - I had to turn the exposure levels all the way up in Aperture to see the stars and the silhouettes of trees. So there is definitely room for increasing exposure time without getting too much glow from ambient light, but I guess I'll just have to play with it to see how much I want to increase it. Maybe a few minutes at least? That would also help with the airplanes, as you said. Unfortunately with the weather here in Chicago its likely to be quite awhile before I can try this again. The ones I posted so far were all taken over break in California, which was usually dry and clear even for there this winter.
Regarding dark frames, I did take a dark frame picture by hand and I put it into StarStax and tried to get it to subtract it, but it wouldn't work and I'm not sure how else to do it. With the 15 sec exposures there were only a couple hot pixels that were noticeable, so I ended up just removing them in Aperture by hand in the final photo, using the repair brush (I may have done that after I posted them to flickr, when I decided to make prints, so I'm not sure if those versions still have the hot pixels or not. Either way you really have to look closely to notice them.).