Coming to this a few years later, took me a while to figure this out, and I didn't do it exactly as Nathan indicated, but close enough, and I thought I'd explain a bit more.
The idea here is that you're going to get a mesh object (like a UV Sphere EDIT: Cube works better see below) to follow the path using the Curves modifier, like in this video: https://www.youtube.com/watch?v=oHkzyH9dpv4
You need to ensure that the mesh object uses the Curves modifier properly, I used the Z axis as the "deform axis" (EDIT: Any axis works, I now like to use Y since it's closer to the G key) Before you apply the modifier, you'll have to use Alt-G to clear the locations of both the curve and the UV sphere so that they're both at the world origin. I'm sure there's a different way of doing it to make it work, but I'm new to this, and world origin was the only way I could get it to work.
After that, you can use the Z location attribute to move it along the curve
Notice that only the Z value changes under the Transform properties, so it works really similarly to the "Follow Path" offset and can be animated and keyframed.
Next, you vertex parent (NOT regular parent, it won't work) your camera to the UV Sphere (I didn't do it perfectly because I'm new to using parenting properly) but it works pretty fantastically and allows me to get all the shots I want!
Now when I extrude more camera path curves or adjust the points, the UV Sphere (and attached camera) stays right where I want it to.
EDIT: I've come back to this a few years later and wanted to add more clarity. I'll list out the steps completely here:
- Create bezier curve
- Create a mesh object, a cube works best
- Modify the cube by deleting all faces and creating a edge connecting two of the corner vertex points. Subdivide this edge so there's a point in the exact center of the cube. This is important for later because when you vertex parent the camera to the cube, it will select the nearest vertex, and if you don't have a vertex at the center of the cube, it will connect to one of the corners, which will create a strange offset.
- Add a camera to the scene
- Set the curve, cube, and camera to world origin by clearing position (Alt+G)
- Select the Camera first, then the cube and select Parent > Vertex. Since both the camera and the cube are at the same location, the vertex of the camera should perfectly overlap with the vertex you created at the center of the cube, so when you vertex parent, you shouldn't see anything visually happen. However, after this step, if you move your cube, your camera should move with it
- Select the cube and add a curves modifier to it. Set the bezier curve to the target object and the cube should immediately jump to be on the curve, bringing the camera with it. I like to set the Deform Axis to Y since it makes moving it simpler.
- To move your contraption, select the cube and move it by pressing G, then press Y to constrain the movement to the Y axis as specified by the curves modifier.
- You can now keyframe your camera by keyframing the Y value on the cube location.