There's another easy route, HEL-LAX-LAS and I would personally try to claim for ORC, but I do not know if that's foolproof. Maybe someone else will be able to chime in.

Alternatively, I never have been able to route a TP run the route you're doing, so I don't know how you got it in the first place... However something like HEL-LHR-JFK-LAX-LAS is normally allowed as far as MCT and avoiding overnights goes. The bottleneck is that there's only few services between HEL and JFK, whereas with heathrow it's a lot easier.