Define:
"schools with poor internet connection"
in technical/network terms.
There is a term called 'last mile' ... that's the connectivity between the server to
the browser requesting the content.
Student A - uses a local telco connection to the internet.
The server they are going to at the school might be on that same telco network but then again it might be on another network.
On internet, one does not go straight from point A - the students location - to point B - the server unless they are one the same TCP/IP network - probably a 10. wide area network.
So another example: Student A is connected to Telco called 'FastInternet' via their computer which goes through a home router to upstream 'FastInternet'. The local school server is hosted on another network called InternetSchools'. They are not the same network.
For Student A to get to the server there are other routers - 10 hops away - which is really good, BTW, to get to the moodle server.
The more hops the slower it is.
You, as the moodle server admin, don't control the networking layer of that.
How you could see this:
From a computer where Student a is connected, use a terminal program that can to a 'trace route' and point trace route to the IP address of the Moodle server.
Also, from your server, do a traceroute from the server to the IP address seen by
the moodle server for Student connection.
Those trace routes happen in milliseconds and each packet of info has a time to live built into the packet. If a packet doesn't reach destination within 30 tries, the packets kill themselves - thus breaking the connectivity between Students location and the Moodle server they are trying to go to.
Moodle content is comprised of the .php scripts that point to files contained there in.
Example: link to an .mp3 audio file in a course.
That .mp3 file is stored in a sea of files moodledata/filedir/ but not by it's humanly recognizable name - cool.mp3 - but rather a content hash value which looks like
sa34dbwerwf334fdsasdjedaghasdfas
a bunch of alphanumeric characters.
Taking the example above:
In moodledata/filedir/ there is a sa directory and inside it there is a 34 subdirectory
and inside that resides a file named for the contenthash: sa34dbwerwf334fdsasdjedaghasdfas
Moodle users see the link to it as cool.mp3 but that name and file extensions comes from the meta data - the same row in the database that has the contenthash value - a humanly recognizable name ... cool.mp3.
H5P activity is a different beast ... H5P has modules to itself ... like little players
for content types. The entire activity has an .h5p file name extension, but contained there in could be a link to a 'cool.mp3' audio or the 'cool.mp3' file is included in the .hp5 file itself.
Rsync does files. It does NOT do specific rows in a table of a database.
Relatively addressed links to large files is possible with moodle, but one has to use file system repo setup in moodle.
Your content development server has a directory outside of moodledata/filedir/ we'll all 'multimedia'. 'multimedia' has sub folders/directories ... audio, video, etc.
Inside those related files ... all .mp3 files are audios and go into the multimedia/audio/ directory by humanly recognizable names ... don't use spaces/caps etc in the file names - just alphanumeric characters.
In Moodle to provide a link to that file, would be done via Moodle's file system repo which is pointed to '/var/www/multimeais' with subdirectories of audio, video, etc.
The link built in the moodle interface - resource is the file system repo drilled down to the subdirectories and specific file name - important that you use 'alias' That prevents the multimedia file from being copied into moodledata/filedir/ It then is a relatively address link to a file.
On you school moodle servers ... they would have the same structure ... a '/var/www/multimedia/' directory with same sub directories. The course backups make then hopefully would in include the alias to the humanly recognized file in the file system repo on the school server.
NOTE: that will speed up access for students ONLY ... ONLY when the are at school. NOT the 'last mile'!
You still do specific content links in backups of courses and add those to existing courses, but you also rsync the /var/www/multimedia/ directory progressively ... meaning you rsync only new multimedia files that don't exist in the school multimedia directory.
Mind boggling isn't it! 
If you can find info, check out how Discovery Education (DE) works with local servers - and 'last mile'. What I've tried to describe above is kinda what DE does.
'SoS', Ken