I think there is no any "pioneer" work in your case. There is a problem and you have a special environment. You can of course look on another forum for tips, but I do not think you will find much better tips. Anyway, if you have a solution you can inform us too.

Rsync can be hardly implemented in bash, it has a lot of features. As far as I see you need to develop some script to achieve your goal. Why didn't you try the tip I gave you:
first step copy rsync bynary with ssh to the target host, second step: use rsync over ssh. Just remember, any other solution will be much longer and much more difficult.

The first thing that you always should do when trying to write a script or program is to break down your problem into smaller sub-problems.

For example, your backup problem can at first be divided into two sub-problems:
- the actual backup
- the removal of files that no longer exist on the source

You can break down these sub-problem into smaller problems:
Backup:
- find files which have to be backed up (pretty easy if the backup is scheduled on a timely basis, for example every 24 hours, just find all files with a newer creation/modification time, find can do that)
- copy them with preserving the path (the --parents option of cp can do that, can also be done using tar or cpio)

Removal:
- find all files that are potential candidates for removal in the backup folder (files that are younger than the last backup have just been copied by you, so you need only to check files that are older)
- check if those files exist under the same relative path in the source directory (a case for Bash parameter substitution and the test command), if not delete the file in the backup

With breaking the problem down this way it shouldn't be that hard to come up with a Bash script for the wanted functions.

But I thought you are using busybox and bash is not built into busybox. So if you can install bash, why can you not install rsync?
--- rod.