Faster way to do an Update which includes a window function

Question

I am looking for a faster way to do a update query which includes a window function, and don't have any solid idea what might help.

I am "denormalizing" a bit of data, which means moving the grandparent id into the child, and adding a sequence number. Prior to this we had no "grandparent" (crate) level, only "parent" (box).

The schema is quite simple, in this case:

crate[id] => 
    box[id] => 
        unit[id, sequence_in_box]
           adding [crate_id, sequence] to `unit`

The query I have runs fairly slow (to me), only updating around 10k rows a second (200k rows, ~22 seconds). Since some instances of the database have 2M rows, I'm hoping to make this update go a bit swifter.

UPDATE unit dest SET
    crate_id = src.crate_id,
    sequence = src.sequence
FROM (
         SELECT u.id, b.crate_id, row_number() OVER w AS sequence
         FROM   unit u INNER JOIN box b ON u.box_id = b.id
         WINDOW w AS (
             PARTITION BY b.crate_id ORDER BY b.id, u.sequence_in_box
         )
     ) as src
WHERE
    dest.id = src.id

Sample Existing data (with desired update) looks something like this, with some field names abbreviated.

crate    box            unit            
id       id, crate      id   box  seq   crate_id, sequence 
-----    ---------      --------------  -------------------
1        1   1          1    1    1     1         1
2        2   1          2    1    2     1         2
         3   2          3    2    1     1         3
                        4    2    2     1         4
                        5    3    1     2         1
                        6    3    2     2         2

I can't use UPDATE x FROM because window functions aren't allowed in an update statement (and I'm not sure that would be faster anyway.) I am prepared for a "nope, no better way", just hoping its not true :D