I don't have time to research your cities and dates right now, but in half a dozen similar situations over the past few months the best deal for paid tickets has been (by several hundred dollars) a flight to London followed by a partner ticket onward. With AA or BA you ask for a Visit Europe Pass ticket. *A has a similar program. You have to get these in North America in conjunction with a trans-Atlantic flight on an alliance member.

The usual online booking places don't have these fares. You have to call the airline and ask about them.

The reason this works is that competition to the UK keeps those fares low, and the intra-European fares in these programs are designed to compete with European bargain airlines.