@The_Director, Thanks for the offer of help! I've got some craziness these next few weeks with church and family obligations, but I'll certainly keep that offer for help in mind for when the schedule lightens up.
Rather than green screen the Blender renders, I'm just doing it all in Blender. In the above picture, the background is black, while the stars are particles in the scene. This seems far better than bothering to render, then match the camera motions and try to add stars in Vegas. I did take your advice and set the resolution up. Thankfully, the GPU tip is one that I saw before. You're right, it does help! (Not much, since my laptop isn't built for heavy graphics, but every little bit is nice.)
Raytistic, Right now, I've got the samples sitting at 1,000. It's taking roughly 10 minutes a frame, which is killer when the clip is 140 frames long. I tried with higher samples before, but it was simply far too slow for my liking. The lighting setup has been adjusted since that frame was rendered, things aren't as dark and grainy anymore so 1,000 samples may suffice for now. However, you're right, it would help the quality.
Other than rendering the newest draft of the scene, which can be done at night or while I'm at work, little will be done with this through the holidays. However, it's been a great learning experience. Thank you to all for your tips and encouragement! I'll be sure to post the video whenever it's finally done.