Hi Jeff,
you could use CLI: https://docs.moodle.org/28/en/Administration_via_command_line#Upgrading .
Keep care of running CLI tools with the same user under which the web site hosting your Moodle instance is running otherwise you'll end up w/ several file permission issues.
Besides, look at the software requirements because in your 3.x migration path you need to add an extra step if you want to go further 3.1 i.e. moving PHP from 5.6 to 7.x i.e 7.0 for 3.1 and not 7.1 since it is not supported by 3.1; if you want to go further PHP 7.0 for security purposes - which should be required - you need to break your migration path in between 3.1 and 3.2+: https://docs.moodle.org/dev/Moodle_and_PHP7.
HTH,
Matteo