pt-online-schema change and DB Backups, how to handle backups during schema change?

I have a MySQL database that is hundreds of GB in size and it requires an alter. Normally mysqlhotcopy is used for a full backup once a month and the binary logs are used for incremental backups on a daily basis. Based on my tests the pt-online-schema-change run will take almost 5 days on my system. The toolkit is great in that it keeps my system up and running the whole time but during this time how should I handle backups?

A full backup would double the backup size as the temp tables would be backed up as well. The tool disables binary logging so there are no binary logs to grab either. Anyone have some tips for handling backups during long alters?