This is potentially what you're looking for in setting up the test board; if an particular extension or other change you use on your production board has an issue with the later phpBB version, now is when you can identify that condition ahead of time.
The 500 error means something failed in a way which doesn't even let phpBB handle or report the error, and the error will actually be reported by the web server itself. (e.g. in the Apache error log, which might be just an error log in your main site directory, or might be something you access through your hosting control panel.)
The error log will tell of a particular failure, a particular PHP call stack, or a particular configuration issue, etc., that resulted in the 500 status. That's the next clue to look for: What did the web server say the cause of this 500 status was? You can include the latest log entries here for input on what kind of issue they're reporting.
It might turn out to be something more unique and limited to "just your test environment." Or it might be a clue of something you'll now know to address ahead of time and avoid when updating the production server. (e.g. An updated extension that needs to be installed before updating to phpBB 3.2.7, or similar.)