I don't see why this is any kind of issue. Every Bond auditions to lines written for Connery (specifically the seduction scene between 007 and Tatiana in From Russia With Love) The words don't matter, it's the delivery.
I agree. A good actor will put their own stamp on the lines. My recollection is that RTD said that he pretty much wrote the 10th Doctor the same as the 9th but that Tennant made him sound and act different from Eccleston.
I read the audition lines in my head in Smith's voice but that's because he's been such a distinctive Doctor and the most recent one I've seen (the scene is also admittedly quite like the 'fish fingers and custard' one). But I'm not an actor. A good actor will come in, put their own spin on it and make it sound like the Twelfth Doctor.