Here is a Load Remover and Auto Splitter for the Inside Out playset. It will automatically start when entering a level from the level select screen. It will split at the end of every level (including the final level) when the level status screen is dismissed. And it will remove load screens.

Download and save the InsideOut.asl file to your Livesplit's Components folder. To use it, add a "Scriptable Auto Splitter" to your livesplit layout, and select the InsideOut.asl file in the settings. Make sure you set livesplit to compare against Game Time to see the loadless time.

(Will be integrated into Livesplit by default whenever I figure out how to do that)