I know this is a bit old, but I've just started creating a LiveSplit plugin that might help this situation. It uses the LiveSplit server function to sync two instances of livesplit. It's ideal if you use 2 PCs to stream but still want to use an in game timer or autosplitter

Here's a link to the github page. The readme has all the instructions https://github.com/Villhellm/LiveSplitClientPlugin