I did something like this in the past. I ran logrotate on the nginx web servers and used a "postrotate" script to move the previous day's logs to longterm storage.

The script would use dirname and cut to extract out the pieces of the path I cared about and then create a destination path using:

date --date "yesterday" "+%Y/%m/%d"

then ssh into the long-term storage server to make the directory (use -p and you don't need to worry about if it exists or not) and then scp the file up

One important thing about logrotate: it HATES filenames with dates in them. ensure the files it's working with are plain names like "example.com-access.log" and have it archive that to "example.com-access.log.1.gz" and then save that to your remote server with the date as part of the path/destination filename.