Being a plugin developer myself, I would recommend the following procedure:
- If you have contrib add-ons (plugins) then before upgrading, check and download the version for the version of Moodle you are upgrading to. If there is not a version, then remove it before upgrade and perform corrective action if required. If there is an upgrade then read the 'readme' first to check for any special instructions.
- Turn on 'Maintenance Mode' and perform a complete file and database backup.
- After completing the above, update Moodle and the plugin's at the same time, then you should not get the 'reloading' issue.
- If you do get the 'reloading' issue, then go to the plugin's folder in your installation and update the files from the downloaded version you got in step one. It is always much safer to backup and clean out the plugin's folder before putting in the new files to avoid conflicts. If a plugin has database tables then it should cope (if not contact the author) - and if fail, remove the plugin both file and it's entry in the 'config_plugins' table (read it's uninstallation intructions in it's readme file - if none - contact the author and ask for some). Once you have updated all the plugins causing the issue, go back to the 'reloading' page and 'reload' to continue to complete the upgrade.
- Turn off 'Maintenance Mode'.