However you will always pick up some jitter,
He could always use an LPC ARM, they can be set to have jitter-free interrupts 
At 12000RPM he has 5mS between pulses and the pulses don't look to be very long so most of that time is spent waiting for the next pulse or, writing to an LCD or calculating a pulse width.
LCDs are slow but I think if the data for it is put in a ring buffer and for example one byte sent every in inter-pulse period that shouldn't get in the way.
I'm thinking pseudo code like this
loop {
wait for trigger
do pulse
calc value
write stuff to LCD ring buffer if necessary
read a byte from ring buffer and send to LCD
}
No interrupts required (and disable any default interrupts) and "wait for trigger" is a tight polling loop.
Rob