FanFiltration said:

You first see the shuttle fling next to the bridge, then the HQ shot from ST-IV (shuttle flight angle adjusted), then cut to shuttle entering tram station, Kirk exits shuttle and we cut just before he sees Commander Sonak.

Alright, here's the shots FF mentioned and what needs to be changed.

In the top shot, we have Kirk's shuttle headed towards the tram station, then in the second shot its headed towards the camera. FF wants to use this shot of Starfleet command and Kirk's shuttle flying past(?) it. Then the shuttle lands in the tram station.

I think we can go about this two ways.

The first is modifying the existing mattes. The tram station needs to be replaced with Starfleet Command in the top shot and the bridge needs to be moved in the ST4 shot because the angle is wrong to the rest of the shots.

We can scrap the existing mattes and make all-new ones. Replace the tram station with Starfleet Command, make an all-new Starfleet Command using compilations from the rest of the series (I would love to see something based on the shots of it from TNG).

Here are some resources:

Starfleet Command in ENT (complete with Google Map location! The tram station could be that building on the right of frame if we wanted it to be)
Starfleet Command in ENT from orbit (not seeing how to reconcile the two though, as there are no round buildings here)
Starfleet Headquarters from TNG (this is the iconic building)
Starfleet Academy in TNG (also within view of the Bridge)
Starfleet Command Destroyed in DS9
Replica Starfleet Academy from VOY
Replica Starfleet Academy from VOY (sixth picture on the page)

Note that all of these look like they're right on top of one another. These are really just to give an idea of Federation architecture (which doesn't seem to change much over the years, so we can pull from the best of these).