Difference between full JPEG and headers+abbreviated

The libjpeg library I have been using supports creating "abbreviated" JPEGs which basically means that one can create a sequence of JPEGs that all share the same headers.  This cuts down on disk size.  This is what I have done with the .LDIMG file format.  But now that I am working with hardware decoders that apparently have no concept of this, it becomes my challenge to recreate the original "full" JPEG from the "headers" and the "abbreviated" JPEG.  Here is a file compare of how the headers and abbreviated content relate to the full.  As you may be able to see, it appears that a careful algorithm can do this reconstruction fairly simply without having to understand the JPEG header format at all.  At least, that's my hope as I do not want to spend time understanding the JPEG header.