There is not currently an option to automatically update the headers while running Image_Menus->Process->"Combine stack
slices into single image".
However, if you update to the latest "daily build" version of AIJ, there is a new option in Image_Menus->Process called
"Copy FITS header to this image", which allows you to do just that. Future versions of AIJ will provide an automatic
default copy, but it must be done in a separate menu selection as of now.
That said, unless your combined images were perfectly aligned, I would plate solve again, even after copying an example
header, particularly given the work you mentioned that you are doing.