Latest update... I went on a second European tour with a single purchased itinerary on United. This time the return flight from Salzburg originated on Austrian/Lufthansa (United's code-share partner). First they claimed that I needed a "reservation" for a properly packed bike box whereas United doesn't. After about 30-45 minutes multiple phone calls and a lot of hemming and hawing (slow day at the airport) they finally decided that I could put the bike on the plane. However, they decided that I needed to pay an arbitrary 200 euro "excess baggage" fee. Not wanting to leave my bike in Salzburg I reluctantly paid the fee.

I am currently disputing the charge through my credit card. We'll see what happens.