It seems somewhat unusual that the meter is emitting a pulse - normally, the pulse is less than one second, usually 100 - 200 ms, in length. The pulse length should make no difference to the operation of the sketch, because it works on the falling edge of the pulse.
That calibration in emoncms looks OK to me, but I’m not an emonCMS expert.
Most meters emit a pulse when a quantity of energy has been consumed. In that case, the pulse rate is proportional to power, the pulse count over an interval is proportional to the energy over that same interval.
On that basis, “Keizan Power Pulse” should be a number that continually increases, like this:
The slope is power, the absolute value is energy.
I’m struggling to read the text on that screenshot of the graphs, but that’s not what you have,
so it would appear that what your meter is sending is not what you think (and not what the pulse counting firmware is expecting). And what you originally wrote “50000 pulses = 2.4 kW” actually looks correct - the pulse count is proportional to power. This is most unusual. In the light of this, I think you need to go back to the meter’s data sheet and check exactly what it says.
I think you might need to redesign your LED drive circuit. I’ve just realised that it’s probably counting mains cycles while the LED is on, because the LED and diode in parallel imply it’s fed from a.c. and the LED is flashing at mains frequency!
You need to provide the LED with a smoothed d.c. supply.
(There is in the software a delay to ignore contact bounce, but it’s ineffective if the LED is flashing at 50 / 60 Hz for several seconds. What will actually happen is when the LED goes off, it counts a pulse and a 110 ms timer starts. It will then ignore the falling edges when the LED goes off 20 ms later (assuming 50 Hz), 40 ms later, etc up to 100 ms later, then it resets and counts the next falling edge at 120 ms as a pulse and starts again. So it is counting 1 pulse for every 6 mains cycles while the LED is apparently on continuously.)