Hi,
Basically the calculation is right. Well done.
Still I want to comment it.
* you calculated the input side first, then the output. There's nothing wrong with it, but often it's the other way round: You want to drive a given load. In your case the 10k, plus some overhead current.
(The usual way is to determine R2 first ... according voltage levels, speed and safety margin)
* you used a CTR of 135%. This is rather optimistic. I see the CTR can be as low as 50%. And you may expect it to degrade with the years, with temperature...and for switching applications (saturated) you should calculate with even less ctr. I'd rather use "safe" 25%.
* you calculated R2. The value you calculated is the "minimum" value for optimistic CTR. So it's not good to use this value...always use a higher value resistor to get reliable operation. If switching speed and voltage levels are good, then stay with the initial 10k.
The issue comes during pulses when frequency affects the performance
You did not mention "pulse" nor "frequency" before, thus I thought of a DC application. For sure frequency and waveform has a big impact on operation.
What's the expected waveform (square wave, what duty cycle range, what timing accuracy) and what frequency do you need?
Btw: I think it's still a good idea to give us all informations requested in post#4.
Now you talk about LTspice... why don't you show use the used schematic and the LTspice results?
Klaus