Indeed the infamous o-rings sealed connections between pieces which logically wouldn't have been separate.

I believe this is incorrect. If I remember correctly, transport was not the only issue with building the solid rocket boosters in one piece: physically pouring a solid rocket motor of that size was infeasible.

I of course don't remember the details so I looked them up. Here's an interesting document that doesn't actually go into the fundamental question of why the engines were built in one place, partially assembled in another, then snapped together in a third:

http://www.cedengineering.com/upload/Ethics%20Challenger%20D...

The point being that if the rockets were welded and fueled near the launch pad there would have been no need for o-rings. The reason for o-rings was that cylinders full of fuel needed to be shipped around and welding them together would have meant too big a lump of explosives. Casting a big engine had nothing to do with it.

That's definitely part of the B1-B program.