This is where the experts are required I fear.
I don't think that 4 routing codes ever work for me so there may be a 3 limit. I would try removing one of the routing points at a time, one way only, and insert HEL. If you get a result, try the other direction. Ordinarily, I'd break the route up in Multi-City, and search from there....I tried this for the basic LHR JFK LAX route and couldn't get the same flights that worked in Return to work in Multi City, but that could be operator error.
As I say, an expert may be along shortly. Me, I just spend hours trying every possible combination....