there are 2 ways of doing it. one is to simply put all the images into BPP. the script will calibrate, debayer (when "CFA images" is checked) and register all the images to the reference image. assuming that succeeds, you'll have a bunch of c_r.fits images (or c_d_r.fits if debayering was used) that are all aligned to the same reference image. BPP will also integrate all the images, which may or may not be what you want. but you can throw the integrated result away of course.
then you can stack the different exposure length groups together using ImageIntegration. and since they are all already aligned to one another, you can then take those masters and put them in HDRComposition.
however, if you do as you're describing, yeah, you'll have multiple integrated images which are not aligned to each other. so then you have to register those using StarAlignment, before proceeding to HDRComposition.
but in your original message, it sounded like BPP failed to register all the images. so i was suggesting ways to try to debug what happened. SA has a mode where it shows you where the stars are that it detected in your image. you can use this mode to see if it's picking up on hot pixels instead of stars, or if finds too few stars, or what. the dropdown menu in one of the upper panes of SA has a mode selection. "detected stars" is the special mode that just shows you what stars were detected in the target image.
rob