So I'm readdressing the issue. Something odd seems to be happening the moment your ship passes the station's dock threshold. Here's some screen shots to demonstrate.
Here, I've lined up the view with the dock.

Zooming in now, still outside the station bounds, all OK so far.

Here, I'm *just* outside the bounds of the dock.

And here, I've *just* crossed over the bounds to be inside the dock.

The important thing to note on that last screenshot is that you can still see the docking port flashers in front of you (the ones on the back wall of the dock, and a couple of the ones on the side walls). Which means, you should be seeing the walls of the dock around you. But instead, they've all vanished.
I've tried a couple of solutions (grabbing docks from other working stations and massaging them into place; creating a black outer case for the dock, slightly bigger than the actual dock, to block the internal view) all without results. I've also checked the dock itself, and I can position myself inside it successfully (using the "Test Ship Model" tool as used in the above screenshots), so the sub-entity itself seems to be OK.
Does anyone have any suggestions on what I should be looking for?