Sounds (to me...) like a perfect case for using segmented memory acquisition.
Acquire in segmented mode then save the outcome on a USB memory stick, in CSV format. All your segments (each with a pulse) will be there. Should work on your Keysight DSOX1102A (it works beautifully on my DSOX1204). Not familiar with that particular Rigol model, but if it has segmented memory it should work too. Of course, you can analyze the segments directly on the screen, one by one, after acquiring all of them.
You might miss some pulses if they are fired faster than the trigger re-arm time (~10us or so). Also, might not be very happy with the resolution (each acquisition will be limited to the total memory of the scope divided by the number of segments - i.e. you'll get ~33,000 data points/acquisition for 300 segments, to a total of 1MB - the available memory on that scope, if I am not mistaken).