could you post a description of your working method to find the particular path you chose?
I think trial and error comes closest

I started from the outside and went in. Whenever I hit scenery, I change the x/y of the camera slightly, and rinse/repeat. Once I'm in, I experiment with what initial speed would be best to fly at, but also one has to experiment with the rate of acceleration too.
Does the path have to be straight, and does the camera have to remain pointing in the direction of travel?
Not really, but it's probably simpler if the path is straight. Besides I haven't got a NURBS routine ready yet.
Speaking of which, maybe there's an open source NURBs function on the internet which takes a set of x,y,z points and a few of other variables, including the position along the curve, and generates the new x,y,z...
Can you automate the slowdown you describe so you always travel at a speed logarithmically related to the distance from the closest surface, or do you do it manually?
Hmmm... you've got to be careful, because surfaces which are 'close', you may want to fly by quickly, and vice versa. Also, there may be a few 'nearby surfaces' you could take into account. As said before, there's also the chance of long drawn out sections where the flyby takes ages to get to the interesting part of a new surface. It's all a bit messy.
Can you start rendering along a particular path, and as you move closer to the fractal detail, decide to change direction based on what looks interesting closer up, or do you have to set the path in advance and let it run?
It's easier to do the latter, but in theory I would be able to choose specific points along the way and change course.
Is there some aliasing going on in the shimmering parts of the video?
I think you're referring to the chunks which appear and disappear. That's an artifact of the rendering (i.e. something I need to improve

). It happens especially when the iteration count is high, because ultrathin surface are being 'undetected' as if they didn't exist sometimes.
Can you transport a light source with you so it casts moving shadows--it almost seems like this is happening with some of the complex chambers on the crust just before we burst through.
Yes, the whole of the outside of the picture is counted as a light source in my rendering routines, hence the constant lit tunnel effect. But I would able to add 'other' light sources too if need be. But rendering time would suffer.
I saw the updates to your skytopia page... maybe you could add iq's big video
.
Thanks, I added a link to the Youtube vid for now.
And again, I would really love to see the path arc once we're inside so we get to see a bit more--you could make it skim close to the inside surface for a while if it's not too hard to search out an interesting path before you start the high-quality render.
I'll probably want NURBs first before I explore this kind of thing. But yes, it would be stunning.