I've added a new Stack Aligner mode that I think will do what you want. First you will need to update to the latest AIJ daily build following these instructions:
After restarting AIJ, you should see version 3.3.1.09 or later.
Open your Image Stack.
Start Stack Aligner.
In the setup panel select "Use single step mode..." and "Allow aperture changes between slices..." and turn off all other options (see the set up screen grab below).
Click "Place Apertures".
Before left clicking to place the first (or only) aperture, *disable* the centroid icon above the image stack (
Zoom in very close in the image and locate the precise RA and Dec that you want to align on. Carefully left click at that location.
Right click to advance to the next image.
Left click again at the new RA and Dec location for the second image. Right click to advance to the next image.
Repeat until you are at the end of the image stack.
Then, if you need to combine all of the images into a single image, use Image_Window>Process>"Combine stack slices into single image..."