If on/off times are the issue, check the diode driver for speed response. The less then 300 mW Laser Diode in most packages is good to 10 to 100 Mhz or more. It is the diode driver that affects device timing more then anything else. You may be hitting the rise/fall and bandwidth limitations of your driver. Most of them become a nasty integrator if you start to push the speed.
This requires a good oscilloscope and a fast photodiode with proper termination at the scope input.
We usually try to find photodiodes with a very small surface area, ie about a square millimeter or less. We reverse bias them to increase response speed, and we load them properly at the scope input. If the scope does not have a 50 Ohm input, we add a BNC TEE and a 50 Ohm terminator on the O'scope input.
Take a look at Thorlabs DET10A and the schematic on its data sheet for an example of a moderately fast detector.
Steve