You may well think this is a fairly straightforward transaction, but there are going to be at least 4 fare bases that will need to align with each other and Cyprus point of sale has some specific ticketing restrictions. So regardless of what you have been told, I would expect this to be a manual ticketing process, the onscreen ticketing tools can't handle a lot of issues. Some online travel agency sites may be able to handle this since they will drive away from the Cyprus point of sale if it suits them to do this. It may actually be an occasion where going to an old fashioned high street travel agents in Larnaca would get the best deal. The other option I guess is to book WTP all the way through, which should work, and then either AUP or UuA the LHR-SEA leg afterwards. Alternatively, book in WTP and then call up within 24 hours to amend the LCA-SEA legs.