rsync is not interested in your short or empty files, but you may be able to ask it to not sync large files, let's look:
https://www.unix.com/man-page/linux/1/rsync/ Yes:
--max-size=SIZE don't transfer any file larger than SIZE
Now, for the big files, you need to script up a find and process to make the exerp or empty files under the right relative paths.
If you make a local clone tree of the original directory tree, modified with exerpts, you can rsync that all, so your script does not have to ssh for every file it creates. A clone tree is a dir on the same device where you make all the same sub-directories and then hard-link all the files of the original tree (and any other inodes including any relative withing subtree symbolic links, but not absolute or relative outside subtree symolic links). When you want a file to be different, you must delete the hard link and replace it with a new, real file. (Only such files, with one link, should be written, else you destroy the original.)