What software to choose for incremental mountable backup?

Question

linux

Hi all!
Initial data:
Ubuntu 16.04.3 LTS server with LXC containers on LVM, EXT4. Sites/small projects in containers. Backup is done like this: the container is stopped, an LVM snapshot is made, the container is started, duplicity makes a copy of the contents of the snapshot to another hard disk, it is later synchronized to another server via rsync and a network directory.
Dislikes :
* Duplicity uses a data cache in the /root/.cache/duplicity directory, which takes up more and more space. I did not find how to turn it off, you can delete it, but it is created every time. There is no sense in it, because. the backup is done to a local disk and the cache does not speed up anything.
* Very stupid on a lot of small files.
* It's not convenient to access individual files from a backup, especially when you just need to "walk" through the directory hierarchy and see what happened a couple of days ago.
What you want:
* Very gently so that the backup can be mounted. It is especially good if it will be possible to mount inside the container.
* Incremental backups
* It is desirable that the backup is a set of not very large (within a gibibyte) files, and not a single "piece".
* Encryption is not required
* Good speed
* No extra files like cache
Thank you!

Answer 1

in bash, all of the above will take about 30 lines of code.