Have you tried to manually update the site, by downloading www.remarpro.com downloading and unpacking the zip before transfering to your own site via ftp/sftp?
If i understood correctly, you suggest to update the wordpress manually.
I’m trying to avoid this method, because my WP version is very old and there may be a lot of changes, so there is a high risk of failure.
For plugins, I use the option to upload manually the zip with the plugin, it would be great if there was an option like this in the update procedure!