Solution I split into small CSV files, applied the tweaks that Shlomi Noach suggested and then loaded each file.
Not the perfect. But it loaded a bit faster. Dumping the original table to a CSV file took less than 1 minute, which avoided the table from being locked during the whole process. A script did the job to load each file, which would be very boring to do manually.
In the end I just had to get from the original table the rows inserted/updated in the last hours and update on the new table.