Keep it simple. If you are willing to sacrifice picture quality for ease of setup, I'd say just focus on the scart connection coming out of the tivo box as your slingbox connection. Since the US 350 probably only came with a composite cable, you'll need to find a composite to scart cable to plug into the tivo. Splitting the hdmi signal will only give you a blank video signal due to the hdcp protection on the tivo box, so the analog scart setup will be the easiest to work with while keeping the hdmi connection from your tivo box to your tv working.
If you want to go down the complicated route, you're looking at something like the hdfury 3 which removes the hdcp protection allowing you to take advantage of the component connection. Forget about the sling 350 hdmi port. It's not going to be useful with the tivo box.
So, just look for a composite to scart cable and plug both cables in, then run the setup choosing composite as your output source.