Moving it to the autumn would make sense. Every year the sporting events take over programming, and every year they get a dangerous rabble of whovians baying for blood because the schedule just keeps getting messed with - there's also the consideration that in terms of franchise opportunities in the US, doctor who makes a lot of fiscal sense, as it's likely to hit higher in the ratings over there for BBC America/Sci Fi as well.
You also have to remember that the BBC owns the property, and not the current round of producers, meaning that while it would be a messy prospect, there's no reason why the BBC wouldn't just actively start recruiting a new team if Cardiff were stamping their feet that much - which would also make sense, as I could have sworn that I heard the BBC were planning on moving a lot of their in-house productions to one location in order to cut costs.