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Partially moving /home to a new partition, leaving some content behind

I have a partition and directory structure that looks like:

```
small partition:
/
    usr
    var
    ... # etc.

large partition:
/home
    shared
        other_stuff
        large_folder
    user_1
        ...
    user_2
        ...

medium partition:
(empty)
```

The other partitions are too small to hold the `large_folder` by itself, never mind the rest of `/home`. Note that `shared` does *not* correspond to a user; it's just an ordinary folder I created under `/home`, mainly so that the `large_folder` contents would be on the large partition.

Now with the benefit of hindsight (my reasons for creating the empty partition were ill considered, and also considering reasoning given in https://unix.stackexchange.com/questions/70700), I want to rearrange things like so:

```
small partition:
/
    usr
    var
    ... # etc.

large partition:
/large_folder

medium partition:
/home
    shared
        other_stuff
    user_1
        ...
    user_2
        ...
```

That is: move everything *except* the `large_folder`'s contents to the medium partition and have the system recognize this as the new `home` mount point, while promoting the `large_folder` to the top level of the large partition.

What's the simplest way to do this? Is it possible without scratch space on a separate drive?