I might suggest the "auxiliary bridge" is in fact the location of the warp core. For one, it would have an unobstructed vertical path for ejection, unlike in the case of a vertical core in the pylons. And its hatchlike elements could be how the fuel tanks are topped up. The drive plasma would fire up along the leading edge of the pylons, then.
The lance-like protrusion underneath the hull could be a sensor element - but it also shares something with the cylinders we see at the corners of Miranda
class roll bars.
So perhaps a supergun, even though we never saw those cylinders act in a gunlike manner on the Mirandas
. Or, as I'd prefer, this cylinder could be a miniature form of the front end of Kirk's ship: this could be the main deflector of the Constellation
, just like the pods on the Miranda
would be its main deflectors.
Also, the big bulges on the underside flanking this "lance" could be the fuel tanks of the ship. That is, instead of the neat multiple "canisters" inside the hull, this ship could have two large volumes basically similar to the tanks of the Galaxy
Just wild suggestions. The ship appears just fine as it is in that latest MSD.