I finally made it to the next checkpoint. Here's a poor photoshop of the plane's general positioning (from memory, unfortunately) as I followed the path that the game recommends:
This chamber needs to be dealt with in two parts.
Between the first two purple bars:
The plane needs to move up and to the left, as in the image above. This is to avoid a rotating, rectangular obstacle that is immediately out of the view of this image. This can be reliably achieved by allowing the plane to get to about 85° (hold on the screen until the plane is almost vertical), and then releasing. The plane will "fall" backwards and to the left at this point. Repeatedly tap the screen at constant intervals to keep the plane at a near-vertical angle, but be careful to not exceed 90° because the plane will enter a loop at that point.
Once the plane is in the left-half of the chamber, you can allow the plane to "fall" to a lower angle (80° - 70°) and then begin tapping again to continue moving upwards. In my attempts, not allowing the plane to recover from the near-vertical position causes the plan to crash in the left wall.
After the first set of purple bars:
Maintain an angle near 75° - 80° to maintain a generally upward motion. Once you get past the first obstacle, you can afford to move the plane into the center of the chamber if you're having difficulty with drifting to the right. There will be two more sets of purple-bars that appear to be there just to mess with the rate you are tapping -- adjust for the brief time you are in them by tapping slightly slower.
There are 3 sets of purple bars in this chamber in total. After the 3rd set, prepare to resume a horizontal angle to safely land at the next checkpoint. If you're too far to the right, you may have trouble landing on the checkpoint because you won't be able to recover a horizontal position before hitting the ceiling, or passing the checkpoint.
