Since 2.361.x, Jenkins requires a JVM 11 to run. Would it be by any chance the reason why it failed in your previous attempts?
I would suggest you to first, backup your installation.
Then, upgrade to 2.346.3, upgrade the plugins. Validates that all works, take a new backup. Then upgrade the JVM used. Take a second backup of the installation.
Then, upgrade to 2.361.4 and the required plugins.
Take a new backup.
At this point, you can upgrade to the latest lts version.
Backups will help you in case an upgrade of a plugin had to change the data structure store in your Jenkins Home.
Hoping this helps.