The exhaust probably stunk because the fuel was bad, not the block ... just my guess.
The 068 is the Ram Air 1, 3 and 400 H.0. Cam. It's plenty of cam for a 350 with stock heads.
I once had a 041 cam in a 400 engine with #48 heads (similar to your #16 heads), and it actually ran worse than the 067 cam without changing anything else. Once you get headers and some head work done, though, it starts to make a difference.
I can't tell you whether you have to tear the motor all the way down. It depends too much on how many miles, what the oil pressure was at idle, how much it was sitting between the times it was driven, and so on. Far too many unknowns. Basically, I would tell you that if the block stays in the car for a head swap, add the new cam, build it and drive it. If you take the block out of the car, tear it down all the way and do it right. Either way, if the lower end gives out on you because you didn't go through it the first time, you're not really out anything except a little bit of your own time.