kick the sinusoidal 5V signal (rectangularized by a comparator) out
This I don't understand, where does the sine wave come from? The Arduino can't produce one and even if it could if you are squaring it anyway there's no point.
with a certain delay.
Can this delay be calculated before you need the pulse? IE from the previous cycle.
If so you can poll the input trigger then do your own while loop to get the delay and another to time the pulse. Then when that's done do all the calculations for the next cycle.
This will have just a uS or two of latency and jitter.
And I repeat, why does anything to do with micros need a float variable.
Rob