I read the requirements but could not find a template, so here is a description of the problem. I have a project based on the "Rotating platformer" example with few differences. The capx is very simple, it contains:
A "Player" object with the "Platform" behavior that moves to left or right.
A "Ground" object with the "Solid" behavior that serves as a platform for the player.
A "GroundSensor" object to trigger the code to change the "Angle of gravity" property of the player.
The angle of gravity changes according to the shape of the ground. The capx was changed to show the problematic shapes only. When the player is on a curved ground, it can't move anymore. This problem happens with all browsers and started on version r260 and is also present on r261 and r262.