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?

The Shuttle cannot even fly straight. The engine thrust has to be tilted.