The Adafruit sensor that you're using isn't operating quite how you think it is. If you read the web page and look at the data sheet (I know, it's in Chinese), you'll see that the response time for this device is only specified as "less than two milliseconds". That's far too slow for your application.
From the graphs in your linked PDF, I would venture to say that the turn-on response (the output going low) of this device is actually pretty fast. Even so, we don't know anything about it's delay before responding, nor how much error there is in that delay for each measurement. However, the graph clearly shows that the turn-off time has a substantial delay. As you mentioned, the duration of the flat part of the output is too long given the diameter and speed of the ping pong ball.
That flat part of the curve is not the result of no light reaching the sensor because the ping pong ball is blocking the transmitter. It is the result of the light level going below some threshold and saturating some circuit inside the sensor, and thus turning on a transistor and driving the output low. After light starts hitting the receiver again, that circuit has to come out of saturation and turn off the transistor, which takes a little while -- about a millisecond according to your graphs. The upward-going curve after the flat part is the RC time constant due to the combination of your pull up resistor and whatever capacitance is seen at that node.
The digital nature of this sensor is confusing you. You would have an easier time with a sensor that has an analog output, especially if it were much faster than the one you're using.
I suggest this one:
https://www.digikey.com/product-detail/en/ams/TSL252R-LF/TSL252-R-LF-ND/It has a turn-on/turn-off time of around 7 microseconds, which is well matched to the sample rate of your DAQ system. It also has an analog output so that you can see what's really going on with the light. You can hook it up in a fashion similar to your existing sensor (three pins: Vcc, ground and voltage output), and it can run from 3V to 5V. These parts are about $3.50 each from Digikey.
At 300 meters per second, your ping pong ball would travel about two millimeters in seven microseconds. The temporal resolution of the signal is actually better than 7usec because that is the spec for the output rise time, from a 10% signal level to a 90% signal level. If you had a faster DAQ system, you would be able to see detail even finer than that.
I've used these parts before and found them easy to work with.