Using the Arduino is too slow
The Arduino is just an AVR like most others. If you can do it with a tiny13 you can certainly do it with a mega328.
I probably did something wrong though,
If you use 4 pulseIn()s in a row
you will get consecutive pulses and there will be the inter-pulse delay between each one so the time taken may be quite long. But if you don't mind missing pulses then
Should have a pretty fast response.
I found something that might work
168 pages of data sheet, what part exactly might work.