Iberia have some mean fares from ORD to quite a few destinations in Europe.
If I were you, I would get the following:

ORD-MAD-AMS
Fare basis: IRTUS
Price : €1588+taxes. Let's say around $2500 all in.
Min stay: 7 days
Max stay: 30 days
Refunds not permitted, changes $300.
best part
Unlimited free stopovers.

Therefore, you get to 2 out of the three places you want to visit, all direct flights in business class and all earning miles. What's more, should you wish to continue into the UK, AMS is probably the European airport with the most direct destinations (certainly so as far as full-service carriers are concerned), and you won't need to put yourself through the London misery.