The shuttle is the only rocket system that put part of the rocket above the payload. Were it not for that fatal design flaw, both fatal flights would have been survivable. The first because the explosion would have done less damage. The second because there would have been nothing above the shuttle from which something could have fallen.

I think @WalterBright is probably right and that the Shuttle design was too compromised to be fixable.

Stacking the orbiter on top of the external tank is a non-starter, IMHO. Obviously you'd have to add engines at the bottom, but now your cost goes up unless you plan on recovering the external tank (and how do you do that?).

And now you need another fuel tank for the orbiter, right? Do you extend the orbiter so it can fit an internal fuel tank? Or do you remove the engines and move them to a separate disposable stage?