Blaise,
I believe that this issue is not about stabilizing footage. The time lapses were all shot on a very sturdy tripod from a similar location each time, and slight framing issues can be corrected with simple position adjustments for each week’s image sequence layer in AE.
The issue I’m encountering is almost entirely due to variation in lens distortion between weeks. When I use the auto-align layers function in photoshop, a single shot from each week’s timelapse can all be aligned perfectly, giving me the final result I’m looking for (except for only a 1 frame for each week – not all 60 frames I need for each week’s timelapse).
I’ve also attached an image of my timeline setup to add further clarity. I’m really trying to figure out what tools can be used (similar to the auto-align function in Photoshop) within After Effects to properly compensate for these variations. I’ve had limited success with CC Lens and Optics Compensation, but even that is dodgy. Since I have had perfect success using Photoshop’s Auto-Align feature, I feel this is entirely possible. However, PS is just not efficient at applying this process to the 600 frames needed per time lapse.

Thanks for thinking through this with me.