Sarcasm is an adjusted stress reaction.

You're entirely correct that the BBC would never chance it. But how about a spinoff? Toss in a plot element like Ten/Hand!Doctor and have him split into several different bodies. (You'd also need several Tardises as well, which might be trickier to arrange narratively. You can have as many Doctors as you like, but the plot demands that there's only one Sexy.)

You could then have them all go off and have several different simultaneous series, Sarah Jane-style, without ever necessarily saying which one was the "main" series---because none of them would be despite what the BBC and audience figures might say. And then have a big unifying multi-Doctor story at season end.

Hell, get Dench, but have her choose to age backwards this time. It worked for River.