For ideal door touch, you must strain right to avoid the wall. Getting a dusty third long jump makes it easier.
Alternative movement
This strat is optimally faster than left side, but its less-scripted nature means it tends to be slower and may be less consistent in practice.
For the wall kick, hold up-right and do a buffered kick into double jump, and start holding up immediately after the kick to strafe along the wall towards the platform. You can also run forwards a bit after entering the room to get the wall kick closer to the platform.