Thanks for doing all of this. How did you find the Bombs On version of the game? I was never able to locate that version.​

Isnt that just this? https://www.speedrun.com/rayman_legends?h=100&x=wdmynxdq

The category is hidden by default but it includes the requirements you mentioned.

Have you tried setting LiveSplit to show Game Time instead of Real Time? That's the first thing that is coming to mind.