From memory, my drone stops about 2.5 metres (8 feet) from a solid object - at least moving up on it slowly. In theory (under ideal conditions), it should be able to stop itself from the standard P-Mode max speed of 50 kph (31 mph).
I recently got caught out when attempting to fly between two trees, having forgotten to turn off the sensors. The
P4P stopped abruptly, before it got past the trees. I was probably doing around 35 kph at the time - about the same as RTH speed, which I've always assumed was set slower in order to improve obstacle avoidance capability.
It does sound like your drone is getting a bit close to your test-obstacle. It won't necessarily hit the obstacle if you approach at a faster speed than you have already tried. It should detect the obstacle and brake from a distance that will allow it to stop.