I agree. The timing isn't great, but last year's Super Bowl made me think that even a non-prime Brady would keep us in contention with a solid run game/D and his mental edge.
As far as best guess, I got nothing right now, it's impossible to predict because of several factors.
I think there's a real possibility that he's worth more to us than to anyone else, and we won't trade him before the draft. If a team offered us a 3rd, what's the point if we think we can get a comp pick 3rd for him later on? You're better off keeping him on the roster and having him as security, then getting that same pick later on.
It really depends on the rest of the market. People look at transactions individually, but they are totally dependent on what happens around it. For example, imagine if Dallas wants a 2nd or 3rd for Romo. I think most teams say no thanks. But if they make him available for a 5th/6th, then someone would probably do that instead of giving up a 1st for Jimmy.
Then there's the Josh factor. If he goes to another team, he'll have some interest for sure. When Josh went to Denver, he tried to get Cassel, but the Chiefs had already struck a deal. If he goes somewhere without a stable QB, he will make an offer.
Bradford really isn't worth a 1st and a 4th in a vacuum, but injury + desperation drove that price up. And I could see BB doing similar if he doesn't get a good deal, just holding onto him until after the draft and potentially getting an unprotected 1st round pick from a team, giving us someone to root against.
But I don't think we trade him for the sake of trading him. We will either get a good offer, or we will keep him.