Crap. I just realized how to make the engines pivot to the ET.
Taper the back end of the shuttle, a bit like it was a C-130. The engines are mounted to the cargo door (aiming backwards when the C-130 door is hanging way down like a ramp). Their fuel connetors go through the bottom of the door, not back into the Shuttle.
During mating (stacking), the door is "lowered" so it's back against the external tank, and the fuel connections are mated. It also pushes directly against studs on the ET to more directly transfer loads during ascent. The upper side of the Shuttle, above the door, is a more tapered version of what was used, and still houses the OMS pods, which don't pivot.
After main engine shutdown, the fuel connections seperate (as was done successfully on every Shuttle mission) and the aft engine door closes, mating seamlessly with the OMS pod to make a much more streamlined back-end to the Shuttle. (Note that when closed, the engines are actually aiming diagonally up and back). During descent and re-entry, the engine door is also the rear body flap.
That would take two bearings and one or two hydraulic cyclinders or screw jacks which are required for the main body flap anyway. It eliminates the horrendously complicated plumping in the back-end of the shuttle, because each engine could make its own direct connection to the ET. It lowers the mass (plumbing is simplified), improves ascent efficiency, transfer loads to the ET more directly, and greatly reduces the drag ratio for re-entry and landing.
The downside, which they probably would've missed, is that any foam coming off the ET would've slammed into the bottom of the opened engine door.