After a first rough alignment (see here), it makes sense to start a second run only using a region of the stack containing the object of interest in all images. By this, the number of detected features will automatically increase even if the standard preset settings are used.
Use the rectangle tool (upper left) to draw an region of interest (ROI) around your object and make sure that the ROI covers the object in all sections. After that proceed with the alignment as usual.
This looks pretty simple, I came across your post after quite a lot of google searching. Thank you.