It is now possible to patch the game so that it displays your final time in milliseconds after each run is finished. Here's how to do it:

1. Go to this page and download the 'GoldenEye 007 - Milliseconds IGT Patch' zip.
2. Inside that zip you will find a file called 'make briefing time show milliseconds (XBLA).ips'. Extract that file and save it to somewhere handy (e.g. the 'Bean' directory which also contains your default.xex file)
3. Download a tool such as Lunar IPS to apply the patch to your unmodified version of the game.
4. Once Lunar is downloaded open it and click 'Apply IPS Patch'.
5. It will first ask you to select which ips to use, select 'make briefing time show milliseconds (XBLA).ips'.
6. It will then ask you to select which file to patch, select your 'default.xex' (make a copy first if you are worried about something going wrong).

This should apply the patch and you can now view all times up to 6 (yes six!) decimal places. Many thanks to Carnivorous for help with this.

IMPORTANT NOTE: All times on the leaderboards will continue to be rounded down to the full second, this tool is simply to help you refine your runs and improve your times.