The 8800 used to have a button that went from "Auto bright" to "Full bright" to "Off" for the screen. The 8310 seems to not have this button anymore.

How can I turn off the screen without putting the phone in standby or key locking it?

That feature is gone in the 8300 series devices.

I have found it interesting that in bright light the screen will increase brightness and in dim light it will dim down. you can try this by standing in a bright area, noting the screen brightness, then putting your finger over the LED indicator. It should dim down. It may take a couple secs to activate.

I think there is a light sensor in there.