Hello, Is your web space for 3.1.x already prepared? Please, work only in your copy, so nothing goes broken.
Based on the code changes (styles), it is also possible to update a style even if you are sure. The design is based on prosilver (last version phpBB-3.0.11). Look the style code changes 3.0.11_to_3.0.13pl1 if your System-Version of phpBB is consistent---
Maybe you're able to make the update itself to manually and also to undergo your customizations even the update. Do you know the style code changes and can apply?
https://area51.phpbb.com/code-changes/3 ... -prosilver
Then same from 3.0.13pl1 to 3.1.0 = change step by step and check each step.
Did you already adapted to the style on 3.1.x? It is not hard ...
and than take a look for the next step:
Perhaps you find an updater. Best wishes!