Although I love the end of time, I do have to agree with you there. I'd like it to be done dramaticly, maybe with the Master planning this for years and years, but I'd like the dr and the viewers not to have a clue about the regeneration happening until abotu a few months before (the dr not included). Although what I would like to see done is a cliffhanger like they did in the stolen earth where we all thought the doctor was going to regenerate. Maybe have no one in the public know that the doctor is regenerating, and after the episode, have them announce that this is for real, and we all have to guess who the new doctor will be. Maybe do that and then split the series in half so we're guessing for months, and even right up until the episode itself, no one will know. That'd be a really fun way of doing it, might be a bit annoying, but fun none the less.
Such a thing would not be possible. The departure of a Doctor and casting a new one are pretty big deals. There's no way for the BBC to practically stay silent about it. All it would take is for some tabloid to get wind of it, and prepare a report. BBC obligates itself not to lie to the public so they couldn't deny such a story. Indeed, the only legal way they can prevent the tabloid from running the story is to issue a public statement themselves effectively pre-empting the tabloid. This is the sort of thing that led to Eccleston's departure being announced before S1 finished airing, or Catherine Tate's return in S4 being announced before S3 finished airing.
Rest assured, when the Doctor regenerates, it won't be a surprise. It will be known, it will be hyped. Which is how most people knew Tennant wouldn't really regenerate after The Stolen Earth.