I think we need to know:
1) specifically what airline ticketed this? It sounds like KLM, but you haven't actually said.
2) which airlines actually flew which segments? Were all flights under the ticketing airline's flight numbers?

It seems to me that because this was a technical problem, you'll have to address your issues to the ticketing airline. I don't have tons of experience with this, but it does seem that it should be covered by EC261. The trip originated in Europe, and started out on an EU airline's metal. You ended up hours late in LAS because of THEIR error. I think perhaps your earlier claim was not correctly filed and dealt just with one flight to LAS instead of treating the entire trip as a whole, with an interruption in the middle.

Even if they ultimately deny your 261 compensation, they should at least give you a bunch of miles and apologize for their error.